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 6.4 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 3 and 8 minutes

(b) the response time is less than 3 minutes

(c) the response time is more than 8 minutes

Answer 1

a)

Given :- = 6.4 , = 1.7 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( 3 < X < 8 ) = P ( Z < ( 8 - 6.4 ) / 1.7 ) - P ( Z < ( 3 - 6.4 ) / 1.7 )
= P ( Z < 0.94) - P ( Z < -2 )
= 0.8264 - 0.0228
= 0.8036

b)

P ( ( X < 3 ) = P ( Z < 3 - 6.4 ) / 1.7 )
= P ( Z < -2 )
P ( X < 3 ) = 0.0228

c)

P ( X > 8 ) = P(Z > (8 - 6.4 ) / 1.7 )
= P ( Z > 0.94 )
= 1 - P ( Z < 0.94 )
= 1 - 0.8264
= 0.1736