According to a Monitoring the Future, 56% of eighth-graders actively participate in sports, athletics, or exercising on a nearly daily basis. The Arkansas Department of Health selected a simple random sample of 5,462 eighth-grade students and asked them whether or not they actively participated in sports, athletics, or exercising on a nearly daily basis. ADH then calculated the proportion in the sample who exercise on a daily basis.
a) What is the shape of the sampling distribution of the sample proportion of eighth graders who exercise daily? Justify.
b) What are the mean and standard deviation of this sampling distribution?
c) The ADH finds that of those sampled, 2,998 said they exercise daily. What is the probability of getting a sample proportion of 2998
5462 or less?
