{"type":"doc","content":[{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q1. Identify which type of sampling is used in each scenario: random, stratified, systematic, cluster, convenience."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Types of Sampling"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of different sampling methods used in statistics to collect data from populations."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Random Sampling:"},{"type":"text","text":" Every member has an equal chance of being selected."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Stratified Sampling:"},{"type":"text","text":" Population divided into subgroups (strata), and samples are taken from each."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Systematic Sampling:"},{"type":"text","text":" Select every nth member from a list."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Cluster Sampling:"},{"type":"text","text":" Population divided into groups (clusters), and entire clusters are sampled."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Convenience Sampling:"},{"type":"text","text":" Samples are chosen based on ease of access."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Read each scenario carefully and identify the method used to select the sample."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Match the description to the definitions above. For example, if a sample is taken from each subgroup, consider stratified sampling."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Look for keywords: \"every nth,\" \"randomly selects,\" \"all members of a group,\" \"first items,\" or \"convenient.\""}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Assign the correct sampling type to each scenario, but pause before finalizing your answers."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Stratified sampling"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Systematic sampling"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) Convenience sampling"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"d) Cluster sampling"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"e) Random sampling"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Each scenario matches a specific sampling method based on how the sample is selected."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q2. Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for each variable."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Levels of Measurement"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to classify data according to its measurement level, which affects statistical analysis methods."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Nominal:"},{"type":"text","text":" Categories without order (e.g., nationality)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Ordinal:"},{"type":"text","text":" Categories with order, but no meaningful difference (e.g., low/medium/high)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Interval:"},{"type":"text","text":" Ordered, meaningful differences, no true zero (e.g., temperature in Celsius)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Ratio:"},{"type":"text","text":" Ordered, meaningful differences, true zero (e.g., salary)."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Examine each variable and decide if it is categorical or numerical."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Determine if the variable has a meaningful order or ranking."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Check if differences between values are meaningful and if there is a true zero point."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Assign the correct level of measurement, but stop before stating the final answer."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Interval"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Ordinal"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) Ratio"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"d) Nominal"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Each variable fits a specific measurement level based on its properties."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q3. Determine which type of study is appropriate: Observational Study or Experiment."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Types of Studies"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to distinguish between observational studies and experiments based on how data is collected."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Observational Study:"},{"type":"text","text":" Researchers observe subjects without intervention."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Experiment:"},{"type":"text","text":" Researchers manipulate variables and observe effects."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Read each scenario and identify whether researchers are intervening or just observing."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If researchers assign treatments or manipulate variables, it is an experiment."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If researchers only collect data without intervention, it is observational."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify each scenario, but pause before stating the final answer."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Observational Study"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Experiment"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Experiments involve manipulation, while observational studies do not."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q4. Identify the type of observational study: cross-sectional, retrospective, or prospective."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Types of Observational Studies"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to distinguish between different observational study designs based on timing and data collection."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Cross-sectional:"},{"type":"text","text":" Data collected at one point in time."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Retrospective:"},{"type":"text","text":" Data collected from past records."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Prospective:"},{"type":"text","text":" Data collected over time into the future."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify whether the data is from the past, present, or future."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the study uses past records, it is retrospective."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the study tracks subjects into the future, it is prospective."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the study collects data at a single point in time, it is cross-sectional."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Retrospective"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Prospective"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) Cross-sectional"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"The timing of data collection determines the study type."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q5. Determine whether the given value is from a discrete or continuous data set."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Discrete and Continuous Data"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to distinguish between discrete and continuous variables."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Discrete:"},{"type":"text","text":" Countable values (e.g., number of students)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Continuous:"},{"type":"text","text":" Measurable values, can take any value within a range (e.g., weight, temperature)."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Examine each value and decide if it can only take specific, countable values or any value within a range."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Numbers of people are usually discrete; measurements like weight or temperature are continuous."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify each value, but stop before stating the final answer."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Discrete"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Continuous"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) Continuous"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Discrete data is countable; continuous data is measurable."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q6. Identify whether the given value is a parameter or a statistic."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Parameter vs. Statistic"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to distinguish between values that describe a population (parameter) and those that describe a sample (statistic)."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Parameter:"},{"type":"text","text":" A value that describes a population."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Statistic:"},{"type":"text","text":" A value that describes a sample."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify whether the value is based on a sample or the entire population."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the value is from a sample, it is a statistic."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the value is from the whole population, it is a parameter."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify each value, but stop before stating the final answer."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Statistic"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Parameter"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Sample values are statistics; population values are parameters."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q7. Determine if the events are mutually exclusive."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Mutually Exclusive vs. Not Mutually Exclusive Events"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of whether two events can occur at the same time."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Mutually Exclusive:"},{"type":"text","text":" Events cannot occur together."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Not Mutually Exclusive:"},{"type":"text","text":" Events can occur together."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Consider whether a student can be both types at once."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the events overlap, they are not mutually exclusive."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the events cannot overlap, they are mutually exclusive."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify each pair, but stop before stating the final answer."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Not mutually exclusive"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Mutually exclusive"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Some events can overlap, others cannot."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q8. Determine if the events are independent or dependent."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Independent vs. Dependent Events"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of whether the outcome of one event affects the other."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Terms:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Independent:"},{"type":"text","text":" One event does not affect the other."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Dependent:"},{"type":"text","text":" One event affects the other."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Consider whether the outcome of the first event changes the probability of the second."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the events are unrelated, they are independent."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"If the events are related (e.g., drawing cards without replacement), they are dependent."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Classify each pair, but stop before stating the final answer."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Independent"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Dependent"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Replacement affects independence."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q9. Frequency Distribution Table: Answer the following based on the table."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Frequency Distribution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to interpret frequency tables and calculate class width, total surveyed, and percentages."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Class Width:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\text{Class Width} = \\text{Upper Limit} - \\text{Lower Limit} + 1"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Total Surveyed:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\text{Total} = \\sum \\text{Frequencies}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Percentage:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\text{Percentage} = \\frac{\\text{Number in Category}}{\\text{Total}} \\times 100"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the class limits from the table to calculate class width."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add up all frequencies to find the total number surveyed."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find the frequency for employees with over 20 years and calculate the percentage using the formula above."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculations, but stop before computing the final values."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Class width: 5"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Total surveyed: 50"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) Percentage over 20 years: 16%"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Each calculation uses the appropriate formula for frequency tables."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q10. Find the mean, median, mode, midrange, range, standard deviation, and 5-number summary for the data set: 15, 12, 5, 14, 4, 4, 6."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topics: Measures of Center, Variation, and Location"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to compute descriptive statistics for a data set."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Mean:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\bar{x} = \\frac{\\sum x}{n}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Median:"},{"type":"text","text":" Middle value when ordered"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Mode:"},{"type":"text","text":" Most frequent value"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Midrange:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\text{Midrange} = \\frac{\\text{Max} + \\text{Min}}{2}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Range:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"\\text{Range} = \\text{Max} - \\text{Min}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Standard Deviation:"},{"type":"text","text":" "},{"type":"inlineMath","attrs":{"latex":"s = \\sqrt{\\frac{\\sum (x - \\bar{x})^2}{n-1}}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"5-number summary:"},{"type":"text","text":" Min, Q1, Median, Q3, Max"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Order the data from smallest to largest."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate the mean using the formula above."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find the median by locating the middle value."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the mode by finding the most frequent value."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate midrange, range, and set up the standard deviation formula."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the 5-number summary, but stop before computing the final values."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Mean: 8.6, Median: 6, Mode: 4, Midrange: 9.5"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) Range: 11, Standard deviation: 4.6"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) 5-number summary: 4, 4, 6, 14, 15"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Each statistic is calculated using the appropriate formula."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q11. How many ways can an inspector perform 3 different tests in a certain order from 7 available tests?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Permutation"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the number of ordered arrangements (permutations)."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(n, r) = \\frac{n!}{(n - r)!}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify n (total tests) and r (tests to select)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the permutation formula with n = 7 and r = 3."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate "},{"type":"inlineMath","attrs":{"latex":"7!"}},{"type":"text","text":" and "},{"type":"inlineMath","attrs":{"latex":"(7-3)!"}},{"type":"text","text":" separately."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the division, but stop before computing the final value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"There are 210 ways."}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(7, 3) = \\frac{7!}{4!} = 210"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Order matters, so use the permutation formula."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q12. How many ways can a committee of 4 people be selected from a group of 10 people?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Combination"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate the number of unordered selections (combinations)."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"C(n, r) = \\frac{n!}{r!(n - r)!}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify n (total people) and r (committee size)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the combination formula with n = 10 and r = 4."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate "},{"type":"inlineMath","attrs":{"latex":"10!"}},{"type":"text","text":", "},{"type":"inlineMath","attrs":{"latex":"4!"}},{"type":"text","text":", and "},{"type":"inlineMath","attrs":{"latex":"6!"}},{"type":"text","text":" separately."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the division, but stop before computing the final value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"There are 210 ways."}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"C(10, 4) = \\frac{10!}{4!6!} = 210"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Order does not matter, so use the combination formula."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q13. Find the probability that a randomly selected book is a children’s book."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Probability"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate probability using counts from categories."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P = \\frac{\\text{Number of favorable outcomes}}{\\text{Total number of outcomes}}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add up the total number of children’s books (nonfiction + fiction)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Add up the total number of books (all categories)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the probability formula, but stop before computing the final value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Probability = "},{"type":"inlineMath","attrs":{"latex":"\\frac{160}{260} = 0.62"}}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"There are 160 children’s books out of 260 total books."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q14. If the probability that it will rain tomorrow is 0.20, what is the probability that it won’t rain tomorrow?"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Probability"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your understanding of complementary events."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(\\text{not rain}) = 1 - P(\\text{rain})"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the probability of rain (0.20)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the complement rule to find the probability it won’t rain."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculation, but stop before computing the final value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Probability it won’t rain = 0.80"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Complementary probability: "},{"type":"inlineMath","attrs":{"latex":"1 - 0.20 = 0.80"}}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q15. Probability from a two-way table: Facebook and Instagram"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Probability from Contingency Tables"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate probabilities from a two-way table."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(A) = \\frac{\\text{Number with A}}{\\text{Total}}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(A \\text{ and } B) = \\frac{\\text{Number with both}}{\\text{Total}}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(A \\text{ or } B) = \\frac{\\text{Number with A or B}}{\\text{Total}}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(B|A) = \\frac{\\text{Number with both}}{\\text{Number with A}}"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify the relevant counts from the table for each probability."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the fraction for each probability, using the total number of students (125)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For conditional probability, use the number with Facebook as the denominator."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculations, but stop before computing the final values."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) "},{"type":"inlineMath","attrs":{"latex":"\\frac{50}{125} = 0.40"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) "},{"type":"inlineMath","attrs":{"latex":"\\frac{37}{125} = 0.30"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) "},{"type":"inlineMath","attrs":{"latex":"\\frac{102 + 50 - 37}{125} = 0.92"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"d) "},{"type":"inlineMath","attrs":{"latex":"\\frac{37}{50} = 0.74"}}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Each probability is calculated using the appropriate formula and counts from the table."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q16. Binomial Probability: 47.5% of children prefer chocolate ice cream. If 4 children are randomly selected:"}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Binomial Probability Distribution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the binomial formula for probability and expected value."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(X \\geq 1) = 1 - P(X = 0)"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(X = k) = \\binom{n}{k} p^k (1-p)^{n-k}"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"\\text{Mean} = n \\cdot p"}}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify n = 4, p = 0.475."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For at least one, calculate "},{"type":"inlineMath","attrs":{"latex":"P(X = 0)"}},{"type":"text","text":" and subtract from 1."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For exactly 2, use the binomial formula with k = 2."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For mean, multiply n and p."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the calculations, but stop before computing the final values."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) 0.947"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) 0.354"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"c) 1.9"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Each probability and mean is calculated using the binomial formulas."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q17. Binomial Probability: 85% chance of success, 8 patients. Find the probability of at least 5 successes."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Binomial Probability Distribution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to calculate cumulative binomial probabilities."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(X \\geq 5) = \\sum_{k=5}^{8} \\binom{8}{k} (0.85)^k (0.15)^{8-k}"}}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Identify n = 8, p = 0.85."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the sum of binomial probabilities for k = 5 to 8."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate each term separately, but stop before adding them up."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Probability = 0.981"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Sum the binomial probabilities for k = 5, 6, 7, 8."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q18. Use the Standard Normal Table to find the area or z-score."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Standard Normal Probability Distribution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the z-table to find areas and z-scores."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(z < a)"}},{"type":"text","text":": Area to the left of z"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find z for a given area"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For part a, look up z = 1.31 in the z-table."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For part b, find the z-score corresponding to area 0.0071 to the left."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the table lookup, but stop before stating the final values."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Area = 0.9049"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) z = -2.45"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the z-table for each calculation."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q19. Use the Standard Normal Table to find the area or z-score."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Standard Normal Probability Distribution"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to use the z-table for right-tail probabilities and z-scores."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formulas:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"P(z > a) = 1 - P(z < a)"}}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find z for a given right-tail area"}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For part a, look up z = 1.92 in the z-table and subtract from 1."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"For part b, find the z-score corresponding to area 0.0202 to the right."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the table lookup, but stop before stating the final values."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"bulletList","content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"a) Area = 0.0274"}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"b) z = 2.05"}]}]}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the z-table for each calculation."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q20. Find the critical value needed to construct an 85% confidence interval of a population proportion."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Confidence Intervals"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to find z-critical values for a given confidence level."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"z_{\\alpha/2}"}},{"type":"text","text":": Find the z-score corresponding to the middle 85% of the normal distribution."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate "},{"type":"inlineMath","attrs":{"latex":"\\alpha = 1 - 0.85 = 0.15"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Divide "},{"type":"inlineMath","attrs":{"latex":"\\alpha"}},{"type":"text","text":" by 2 to get "},{"type":"inlineMath","attrs":{"latex":"\\alpha/2 = 0.075"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find the z-score with area 0.925 to the left (1 - 0.075)."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the table lookup, but stop before stating the final value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Critical value: z = 1.44"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the z-table for the area to the left of 0.925."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q21. Find the critical values needed to construct a 90% confidence interval of a population mean with unknown standard deviation if the sample size is 15."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Background"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Topic: Confidence Intervals"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"This question tests your ability to find t-critical values for a given confidence level and sample size."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Key Formula:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"inlineMath","attrs":{"latex":"t_{\\alpha/2, df}"}},{"type":"text","text":": Use the t-table with "},{"type":"inlineMath","attrs":{"latex":"df = n - 1"}},{"type":"text","text":" and confidence level 90%."}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step-by-Step Guidance"}]},{"type":"orderedList","attrs":{"start":1,"type":null},"content":[{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Calculate degrees of freedom: "},{"type":"inlineMath","attrs":{"latex":"df = 15 - 1 = 14"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Find "},{"type":"inlineMath","attrs":{"latex":"\\alpha = 1 - 0.90 = 0.10"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Divide "},{"type":"inlineMath","attrs":{"latex":"\\alpha"}},{"type":"text","text":" by 2 to get "},{"type":"inlineMath","attrs":{"latex":"\\alpha/2 = 0.05"}},{"type":"text","text":"."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Look up the t-critical value for 90% CI and df = 14 in the t-table."}]}]},{"type":"listItem","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Set up the table lookup, but stop before stating the final value."}]}]}]},{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"underline"}],"text":"Try solving on your own before revealing the answer!"}]},{"type":"collapsible","content":[{"type":"heading","attrs":{"textAlign":null,"level":4},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Final Answer:"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Critical value: t = 1.761"}]},{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"Use the t-table for 90% CI and df = 14."}]}]},{"type":"heading","attrs":{"textAlign":null,"level":3},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Q22. Applications of Normal Pro