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. Would it be unusual for 28 customers to purchase magazines?

		No, because it is close to the average number expected.
		No, because it represents 10% of the customers who come to the store on a typical day.
		Yes, because it is more than three standard deviations above the mean of the sampling distribution.
		Yes, because it is two standard deviations below the mean of the sampling distribution.
		No, because it is only 5% higher than the mean of the sampling distribution.

Answer 1

n = 280

p = 0.05

= p = 0.05

= sqrt(p(1 - p)/n)

= sqrt(0.05(1 - 0.05)/280)

= 0.013

= 28/280 = 0.1

= 0.05 - 2 * 0.013 = 0.011

= 0.05 + 2 * 0.013 = 0.089

Since 0.1 is greater than 0.089, so it would be unusual for 28 customers to purchase magazines.

Yes, because it is more than three Standard deviations above the mean sampling distribution.