34% of CSU students participate in the Statistics Games while they attend CSU. You take a random sample of 40 students. You want to determine the probability that more than 15 of them have participated in the Statistics games. Can we use a normal model for the sampling distribution? Why or why not?

34% of CSU students participate in the Statistics Games while they attend CSU. You take a random sample of 40 students. You want to determine the probability that more than 15 of them have participated in the Statistics games. Can we use a normal model for the sampling distribution? Why or why not?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 19SGR

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Question

100%

A. No, because the sample is not random.

B. Yes. This is a binomial distribution, but we can use the normal model to approximate it if the sample is random and the sample size is large enough to have at least 5 successes and 5 failures. np = 40*0.34 = 13.6, and nq = 40*.66 = 26.4.

C. Yes, this uses the sampling distribution of a sample mean, which is N(mu, sigma).

D. No, this is a random variable with a binomial distribution, so we MUST use the binomial distribution to solve the problem.

E. No, because the sample size is not large enough.

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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