Textbook Question
2. Determine whether each number could represent the probability of an event. Explain your reasoning. c. 2.3
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Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.3.22d
22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the
probability of each event. (Adapted from Ipsos)
d. Randomly selecting a British adult who feels that the move has had a fairly positive or very positive impact on Great Britain
Verified step by step guidance1
Step 1: Identify the total number of respondents from the survey, which is given as 1115 British adults.
Step 2: Locate the number of respondents who feel the move has had a 'fairly positive' impact (178) and a 'very positive' impact (134) from the Pareto chart.
Step 3: Add the number of respondents for 'fairly positive' and 'very positive' impacts to find the total number of respondents who feel positively about the move. This is calculated as 178 + 134.
Step 4: Divide the total number of respondents who feel positively (from Step 3) by the total number of respondents (1115) to calculate the probability of randomly selecting a British adult who feels the move has had a fairly positive or very positive impact.
Step 5: Express the probability as a fraction, decimal, or percentage, depending on the context or requirement of the problem.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the proportion of respondents who feel a certain way about Brexit's impact, relative to the total number of surveyed individuals. For example, if 134 out of 1115 respondents feel that the impact was 'very positive,' the probability of randomly selecting someone with that opinion can be calculated as 134/1115.
Recommended video:
5:37
Introduction to Probability
Pareto Chart
A Pareto chart is a type of bar graph that represents the frequency of different categories in descending order. It is used to highlight the most significant factors in a dataset. In this case, the chart displays the responses of British adults regarding the impact of Brexit, allowing for a quick visual assessment of which opinions are most prevalent, such as 'very negative' and 'fairly negative' being the highest.
Recommended video:
04:52Creating Bar Graphs and Pareto Charts
Categorical Data
Categorical data refers to data that can be divided into distinct categories, which can be nominal or ordinal. In this survey, responses about Brexit's impact are categorical, as they represent different opinions (e.g., 'very negative,' 'fairly positive'). Understanding categorical data is essential for analyzing survey results, as it informs how to interpret and visualize the data effectively.
Recommended video:
4:01Introduction to Collecting Data
Related Practice
Textbook Question
Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.
(Adapted from YouGov)
d. Which of the events can be considered unusual? Explain.
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Textbook Question
26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.
d. The person is male or does not wear glasses.
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Textbook Question
Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)
d. Randomly selecting a person from the sample who is either unsure or moderate
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Textbook Question
2. Determine whether each number could represent the probability of an event. Explain your reasoning. d. -0.0004
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Textbook Question
Mental Health A survey asks 4805 parents the severity of the mental issues they experienced from the coronavirus pandemic. The results are shown in the table. A parent is randomly selected from the sample. Find the probability of each event. (Adapted from Kaiser Family Foundation)
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c. The parent did not have major mental health issues or is a mother.
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