Question

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. Which of the following statements is (are) true about the sampling distribution of the sample proportion of customers who buy specialty clothes for their pets at this store?

A. The sampling distribution can be described as a Normal Model.

B. The mean of the sampling distribution is 0.05.

C. The standard deviation of the sampling distribution is 0.013.

D. All of the above.

Answer 1

Solution

Given that,

p = 0.05

1 - p = 1 - 0.05 = 0.95

n = 280

A) sampling distribution is approximately normal, because np 10 and n(1 - p) 10

280 * 0.05 = 14 10 and 280 * 0.95 = 266 10

B)   = p = 0.05

C) =  [p( 1 - p ) / n] = [(0.05 * 0.95) / 280 ] = 0.013

correct option is = D

D. All of the above.