The customer service department for a wholesale electronics outlet claims that 90 percent of all customer complaints are resolved to the satisfaction of the customer. In order to test this claim, a random sample of 15 customers who have filed complaints is selected.
a. Let x = the number of sampled customers whose complaints were resolved to the customer's satisfaction. Assuming the claim is true, write the binomial formula for this situation.
b. Use the binomial tables (see Table A. 1, page 853) to find each of the following if we assume that the claim is true:
(1) p (x ≤ 13).
(2) P(x > 10).
(3) p(x ≥ 14).
(4) P(9 ≤ x ≤ 12).
(5) P(x ≤ 9).
c. Suppose that of the 15 customers selected, 9 have had their complaints resolved satisfactorily. Using part b, do you believe the claim of 90 percent satisfaction? Explain.