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 70% of the cases. Suppose the 16 cases reported today are representative of all complaints.

a-1. How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.) Number of Problems

a-2. What is the standard deviation? (Round your answer to 4 decimal places.)

b. What is the probability 6 of the problems can be resolved today? (Round your answer to 4 decimal places.)

c. What is the probability 6 or 7 of the problems can be resolved today? (Round your answer to 4 decimal places.)

d. What is the probability more than 11 of the problems can be resolved today? (Round your answer to 4 decimal places.)

Explanation / Answer

p = 0.7

n = 16

a-1) Expected value = n * p = 16 * 0.7 = 11.2

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

                                      = sqrt(16 * 0.7 * 0.3)

                                      = 1.8330

b) P(X = 6) = 16C6 * 0.76 * (1 - 0.7)16-6

                   = 0.0056

c) P(X = 6 or 7) = P(X = 6) + P(X = 7)

                         = 16C6 * 0.76 * 0.310 + 16C7 * 0.77 * 0.39

                         = 0.0056 + 0.0185

                         = 0.0241

d) P(X > 11) = P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)

                    = 16C12 * 0.712 * 0.34 + 16C13 * 0.713 * 0.33 + 16C14 * 0.714 * 0.32 + 16C15 * 0.715 * 0.31 + 16C16 * 0.716 * 0.30

                    = 0.4499

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.