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 9.6 minutes and a standard deviation of 2.3 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 11 minutes


(b) the response time is less than 5 minutes


(c) the response time is more than 11 minutes

Answer 1

(a) the response time is between 5 and 11 minutes

(b) the response time is less than 5 minutes

Z = (x - μ) / σ

X = 5; μ = 9.6; σ = 2.3

Z =(5 - 9.6) / 2.3

Z = -2.00 --> 0.228

(c) the response time is more than 11 minutes

X = 11; μ = 9.6; σ = 2.3

Z =(11 - 9.6) / 2.3

Z = 0.61 --> 0.7291

More than 11 minutes is 1-0.7291 = 0.2709

(a) the response time is between 5 and 11 minutes

0.7063