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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 3.Test.5

5. Which event(s) in Exercise 4 can be considered unusual? Explain your reasoning.

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Review the definition of an unusual event in statistics. An event is typically considered unusual if its probability is very low, often less than 0.05 (5%).
Refer to Exercise 4 to identify the events and their associated probabilities. Ensure you have the probabilities for each event clearly listed.
Compare the probability of each event to the threshold of 0.05. If the probability of an event is less than 0.05, it can be classified as unusual.
Explain why events with probabilities below 0.05 are considered unusual. This is because such events are rare and occur infrequently under normal circumstances.
Summarize your findings by listing the events from Exercise 4 that meet the criteria for being unusual, along with a brief explanation for each.

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Unusual Events

In statistics, an unusual event is typically defined as one that has a low probability of occurring, often set at a threshold of less than 5%. This concept helps in identifying outcomes that deviate significantly from what is expected under a given probability distribution, indicating that they may warrant further investigation.
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Probability of Multiple Independent Events

Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. It provides a framework for understanding the likelihood of different outcomes, which is essential for determining whether an event is unusual based on its probability relative to the distribution.
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Calculating Probabilities in a Binomial Distribution

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere random chance. In the context of unusual events, determining statistical significance helps to assess whether the occurrence of an event is noteworthy and not just a result of random variation.
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Parameters vs. Statistics
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5. Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total.

a. What is the theoretical probability of each total from 1 to 11?

b. Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a).

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Finding Conditional Probabilities In Exercises 7 and 8, use the table to find each conditional probability.

7. Business Degrees The table shows the numbers of male and female students in the United States who received bachelor's degrees in business and nonbusiness fields in a recent year. (Source: National Center for Educational Statistics)

a. Find the probability that a randomly selected bachelor's degree-earning student is male, given that the degree is in business.

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66. Access Code An access code consists of six characters. For each character, any letter or number can be used, with the exceptions that the first character cannot be 0 and the last two characters must be odd numbers.

a. What is the probability of randomly selecting the correct access code on the first try?

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"1. What is the difference between independent and dependent events?

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4. The table on the left shows the secondary school student enrollment levels (in thousands by grade) in Oklahoma and Texas schools in a recent year. (Source: U.S. Nation

for Education Statistics)

A student in one of the indicated grades and states is randomly selected. Find the probability of selecting a student who

a. is in ninth grade.

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2. How many possible variations are there in Mozart's Musical Dice Game minuet? Explain.

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