The speed with which utility companies can resolve problems is very important. G

Question

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company; reports it can resolve customer problems the same day they are reported in 68% of the cases. Suppose the 14 cases reported today are representative of all complaints. a. How many of the problems would you expect to be resolved today? What is the standard deviation? b. What is the probability 7 of the problems can be resolved today? c. What is the probability 7 or 8 of the problems can be resolved today? d. What is the probability more than 9 of the problems can be resolved today?

Explanation / Answer

p = 0.68

n = 14

This is a binomial distribution

a) 1) Expected value = n * p = 14 * 0.68 = 9.52

2) standard deviation = sqrt(n * p * (1 - p)) = sqrt(14 * 0.68 * (1 - 0.68))

                                                                   = 1.7454

b) P(X = 7) = 14C7 * 0.687 * (1 - 0.68)14-7

                  = 0.0793

c) P(X = 7 or 8) = P(X = 7) + P(X = 8)

                         = 14C7 * 0.687 * (1 - 0.68)14-7 + 14C8 * 0.688 * (1 - 0.68)14-8

                         = 0.0793 + 0.1474

                         = 0.2267

d) P(X > 9) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)

                   = 14C10 * 0.6810 * 0.324 + 14C11 * 0.6811 * 0.323 + 14C12 * 0.6812 * 0.322 + 14C13 * 0.6813 * 0.321 + 14C14 * 0.6814 * 0.320

                 = 0.5187

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