The customer service department for a wholesale electronics outlet claims 90% 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. Part A Let x = the number of sampled customers whose complaints were solved to the customer’s satisfaction. Assuming the claim is true, write the binomial formula for the situation. Part B Use the binomial tables (see Table A.1in the text) to find each of the following if we assume that the claim is tru:

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Explanation:

Given

Probability of success, p = 0.9

Number of trials = sample size, n = 15

q = 1 - p

The binomial formula for this situation is written as :

P(x = x) = nCx * p^x * q^(n-x)

P(x = x) = 15Cx * 0.9^x * (1-0.9)^(15-x)

(1) For ; P(x ≤ 13).

P(x = 0) + p(x = 1) +... + p(x = 13)

Using a calculator :

P(x ≤ 13) = 0.451 (3 decimal place)

(2) For ; P(x > 10).

Using calculator :

P(x > 10) = p(x = 11) + p(x = 12) +... + p(x = 15)

P(x > 10) = 0.9873

(3) For P(x ≥ 14).

Using calculator ;

P(x ≥ 14) = [p(x = 14) + p(x = 15)]

P(x ≥ 14) = 0.5490

(4) P(9 ≤ x ≤ 12).

P(9 ≤ x ≤ 12) = p(x = 9) + p(x = 10) + p(x = 11) + p(x = 12)

P(9 ≤ x ≤ 12) = (0.001939 + 0.01047 + 0.042835 + 0.128505) = 0.1837

(5) For P(x ≤ 9) ;

Using calculator ;

P(x ≤ 9) = p(x = 0) + p(x = 1) +... + p(x = 9)

P(x ≤ 9) = 0.00225

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