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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
4장, 문제 4.2.9

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Drinking and Driving If one of the high school drivers is randomly selected, find the probability of getting one who drove when drinking alcohol.

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Step 1: Understand the problem. The goal is to find the probability of randomly selecting a high school driver who drove when drinking alcohol. Probability is calculated as the ratio of favorable outcomes to the total number of outcomes.
Step 2: Identify the favorable outcomes. From the table, the number of high school drivers who drove when drinking alcohol is the sum of the 'Yes' column: 731 (Texted While Driving) + 156 (No Texting While Driving).
Step 3: Determine the total number of outcomes. The total number of high school drivers surveyed is the sum of all entries in the table: 731 + 3054 + 156 + 4564.
Step 4: Write the formula for probability. The probability of selecting a driver who drove when drinking alcohol is given by: \( P = \frac{\text{Number of drivers who drove when drinking alcohol}}{\text{Total number of drivers surveyed}} \).
Step 5: Substitute the values into the formula. Use the values calculated in Steps 2 and 3 to compute the probability. Simplify the fraction if necessary.

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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 refers to the chance of randomly selecting a high school driver who has driven after consuming alcohol. To calculate this, one would divide the number of drivers who drove after drinking by the total number of surveyed drivers.
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Introduction to Probability

Contingency Table

A contingency table is a type of data representation that displays the frequency distribution of variables. In this case, the table shows the relationship between texting while driving and driving after drinking alcohol. It helps in visualizing the data and is essential for calculating probabilities and understanding the associations between different behaviors.
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Finding Standard Normal Probabilities using z-Table

Total Count

The total count refers to the sum of all observations in a dataset. For this question, it is crucial to determine the total number of high school drivers surveyed, which is the sum of all entries in the contingency table. This total is necessary for calculating the probability of selecting a driver who drove after drinking alcohol.
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Fundamental Counting Principle
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Phone Numbers Current rules for telephone area codes allow the use of digits 2–9 for the first digit, and 0–9 for the second and third digits, but the last two digits cannot both be 1 (to avoid confusion with area codes such as 911). How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately preceding the last four digits of a phone number. Given both of those rules, how many 10-digit phone numbers are possible? Given that these rules apply to the United States and Canada and a few islands, are there enough possible phone numbers? (Assume that the combined population is about 400,000,000.)

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Same Birthdays If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.

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Computer Variable Names A common computer programming rule was that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BBB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)

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교과서 질문

In Exercises 21-28, find the probability and answer the questions.


Social Networking In a Pew Research Center survey of Internet users, 3732 respondents say that they use social networking sites and 1380 respondents say that they do not use social networking sites. What is the probability that a randomly selected person uses a social networking site? Does that result suggest that it is likely (with a probability of 0.5 or greater) for someone to use social networking sites?

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교과서 질문

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.



Voting Repeat Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 27 Democrats being placed on the first line. The probability of getting a result as high as 27 is 0.029792.

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교과서 질문

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.



Selfie Deaths Based on Priceonomics data describing 49 deaths while taking selfies, it was found that 37 of those deaths were males. Assuming that males and females are equally likely to have selfie deaths, there is a 0.000235 probability of getting 37 or more males. Is the result of 37 males significantly low, significantly high, or neither? Does the result suggest that male selfie deaths are more likely than female selfie deaths?

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