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 8.4 minutes and a standard deviation of 1.7 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

P ( 5 < X < 10 )

Standardizing the value

Z = -2

Z = ( 10 - 8.4 ) / 1.7

Z = 0.94

P ( -2 < Z < 0.94 )

P ( 5 < X < 10 ) = P ( Z < 0.94 ) - P ( Z < -2 )

P ( 5 < X < 10 ) = 0.8267 - 0.0228

P ( 5 < X < 10 ) = 0.8039

Part b)  

P ( X < 5 )

Standardizing the value

Z = ( 5 - 8.4 ) / 1.7

Z = -2

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

P ( X < 5 ) = 0.0228

part c)

Standardizing the value

Z = ( 10 - 8.4 ) / 1.7

Z = 0.94

P ( Z > 0.94 )

P ( X > 10 ) = 1 - 0.8264

P ( X > 10 ) = 0.1736