Question

police response time to an emergency call is the difference between the times 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 responce time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.7 minutes. for a randomly recieved emegency call, what is the probability that the response time will be:a) between 5 and 10 minb) less than 5 minc) more than 10 min

Answer 1

a) 0.8039

b) 0.02275

c) 0.1733

Explanation:

Given that police response time to an emergency call is the difference between the times the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene,

The arrival time of police X is N(8.4, 1.7)

the probability that the response time will be:

a) between 5 and 10 min

`P(5<x<10)\\=F(10)-F(5)\\\\=0.8267-0.0228\\=0.8039`

b) less than 5 min

`=P(X<5)\\= F(5)\\= 0.02275`

c) more than 10 min

=
`P(X.>10)\\\\=1-F(10)\\= 0.1733`