The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy magazines and thinks that he might be able to sell something more profitable. Before making a final decision, he keeps track of the number of customers who buy magazines on a given day. In a typical day his store has 280 customers.
a. Describe the shape of the sampling distribution of the sample proportion. Show that the sample size assumption is satisfied for assuming this model.
b. What is the mean and standard deviation for the sampling distribution of the sample proportions?
c. Surprised by the high number of customers who purchase magazines on a particular day, the owner decides that his 5% estimate must have been too low. Determine how many magazine sales on a typical day would represent an unusually high number (more than 3 standard deviations above the mean)?