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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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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?
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.   
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