AP Statistics Study Guide

AP Statistics Page 1 of 5 Study Sheet: Discrete Probability Distributions

Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright © 1996, Texas Instruments, Incorporated.

These exercises focus on discrete probability distributions and random variables. You’ve seen how to compute the probabilities associated with the outcomes of a discrete random variable and how to create probability histograms to display these distributions.

In this activity, you’ll use your calculator to simulate probability questions of dice rolls and candy sampling. Throughout this exercise, we’ll give you directions on how to conduct the various simulations, produce probability distributions, and create probability histograms.

1. Identify the following as discrete or continuous random variables:

A. Increase in the length of life attained by a cancer patient as a result of surgery

B. Tensile breaking strength (in pounds per square inch) of one-inch diameter steel cable

C. Number of deer killed per year in a state wildlife preserve

D. Number of overdue accounts in a department store at a particular time

E. Your blood pressure

2. A random variable X has the following probability distribution:

X 1 2 3 4 5 P(x) .087 ? .453 .234 .095

A. What is P(2)?

B. Construct a probability histogram of the distribution.

3. A pet shop has two job openings for dog groomers. Of the 10 applicants, 4 live in Bellevue, 3 live in Seattle, and 3 live in Renton. All 10 are equally qualified for the position. Let (x) equal the probability that the 2 who get the job both live in Bellevue.

A. Calculate P(x).

B. Create a probability histogram for this distribution.

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AP Statistics Page 5 of 5 Study Sheet: Discrete Probability Distributions

Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse) TI-83 screens are used with the permission of the publisher. Copyright © 1996, Texas Instruments, Incorporated.

A. Repeat the simulation, described above, 50 times and identify the “likely” outcomes. This may take you a few minutes to complete all 50 trials.

Acknowledgments Question 1: This question 4.77 (a, b, c, d, e) from page 165 of Introduction to Probability and Statistics, Tenth Edition, by Mendenhall, R. Beaver, and B. Beaver. Copyright © 1999 by Brooks Cole, division of Thompson Learning Inc. Further reproduction is prohibited without permission of the publisher.

# red candies (#1s, 2s, 3s, 4s)

Tally Frequency (Tally/50)

0 1 2 3 4 … 18 19 20

Total 50 1.00

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AP Statistics Study Guide