Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.CQQ.9

Chapter 4, Problem 4.CQQ.9

In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.

Find the probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

Verified step by step guidance

Step 1: Calculate the total number of subjects in the study by summing all the values in the table. Add the number of subjects who developed flu and did not develop flu for both the vaccine treatment and placebo groups.

Step 2: Identify the total number of subjects who developed flu by summing the 'Developed Flu' column for both the vaccine treatment and placebo groups.

Step 3: Calculate the probability of selecting one subject who developed flu. This is done by dividing the total number of subjects who developed flu by the total number of subjects in the study.

Step 4: Since the selection is without replacement, calculate the probability of selecting a second subject who developed flu after the first one has been selected. Subtract 1 from the total number of subjects who developed flu and divide by the total number of subjects minus 1.

Step 5: Multiply the probabilities from Step 3 and Step 4 to find the overall probability of randomly selecting 2 subjects without replacement and finding that they both developed flu.

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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 chance of selecting subjects who developed flu from a given population. Understanding how to compute probabilities, especially in scenarios involving combinations and selections, is crucial for answering the question.

Without Replacement

Selecting without replacement means that once an item is chosen from a set, it is not returned to that set for subsequent selections. This affects the total number of items available for the next selection, which in turn influences the probability calculations. In this case, the probability of selecting two subjects who developed flu must account for the reduced pool of subjects after the first selection.

Contingency Table

A contingency table is a type of data representation that displays the frequency distribution of variables, allowing for easy comparison of different groups. In this scenario, the table shows the number of subjects who developed flu versus those who did not, categorized by treatment type (vaccine vs. placebo). Analyzing this table is essential for determining the probabilities needed to answer the question.

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Cloud Seeding The “Florida Area Cumulus Experiment” was conducted by using silver iodide to seed clouds with the objective of increasing rainfall. For the purposes of this exercise, let the daily amounts of rainfall be represented by units of rnfl. (The actual rainfall amounts are in or )

Find the value of the following statistics and include appropriate units based on rnfl as the unit of measurement.

15.53 7.27 7.45 10.39 4.70 4.50 3.44 5.70 8.24 7.30 4.05 4.46

a. mean

b. median

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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.

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