Question

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.8 minutes and a standard deviation of 1.9 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 5 and 10 minutes

(b) the response time is less than 5 minutes

(c) the response time is more than 10 minutes

Answer 1

µ = 8.8

sd = 1.9

a)

                                     

                                      = P(-2 < Z < 0.63)

                                      = P(Z < 0.63) - P(Z < -2)

                                      = 0.7357 - 0.0228

                                      = 0.7129

b)

                          

                           = P(Z < -2)

                           = 0.0228

c)

                            

                             = P(Z > 0.63)

                             = 1 - P(Z < 0.63)

                             = 1 - 0.7357

                             = 0.2643