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 8.0 minutes and a standard deviation of 1.5 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 9 minutes


(b) the response time is less than 5 minutes


(c) the response time is more than 9 minutes

Answer 1

Normal distribution

Mean = u = 8

Standard deviation = s = 1.5

Z-score = ( X - u )/2

a) P( 5 < X < 9 )

Z(5) = ( 5 - 8 ) /1.5 = -2

Z(9) = ( 9 - 8 ) /1.5 = 2/3 = 0.6667

P( 5 < X < 9 ) = P( -2 < Z < 0.6667) = 0.7248

b) P( X < 5 )

Z(5) = ( 5 - 8 ) /1.5 = -2

P( X < 5 ) = P( Z < -2) = 0.0228

c)

P( X > 9 )

Z(9) = ( 9 - 8 ) /1.5 = 0.6667

P( X > 9) = P( Z > 0.6667) = 0.2525