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

solution

(A)P(3< x <8 ) = P[(3-6.4) /1.7 < (x - ) / < (8-6.4) /1.7 )]

= P( -2< Z <0.94 )

= P(Z <0.94 ) - P(Z <-2 )

Using z table   

= 0.8264-0.0228

probability= 0.8036

(B)

P(X< 3) = P[(X- ) / < (3-6.4) /1.7 ]

= P(z <-2 )

Using z table

=0.0228

probability=0.0228

(C)

P(x > 8) = 1 - P(x<8 )

= 1 - P[(x -) / < (8-6.4) /1.7 ]

= 1 - P(z < 0.94)

Using z table

= 1 -0.8264  

probability= 0.1736