Question

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.3 minutes and a standard deviation of 2.7 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer 1

µ = 8.3

sd = 2.7

a)

                             

                              = P(Z < 0.63)

                              = 0.7357

b)

                          

                           = P(Z > -1.22)

                           = 1 - P(Z < -1.22)

                           = 1 - 0.1112

                           = 0.8888

c)

                                     

                                      = P(-0.11 < Z < 2.48)

                                      = P(Z < 2.48) - P(Z < -0.11)

                                      = 0.9934 - 0.4562

                                      = 0.5372