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 10.0 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 7 and 11 minutes

(b) the response time is less than 7 minutes

(c) the response time is more than 11 minutes

Answer 1

solution

(A)P(7< x <11 ) = P[(7-10.0) /1.5 < (x - ) / < (11-10.0) / 1.5)]

= P( -2< Z < 0.67)

= P(Z < 0.67) - P(Z <-2 )

Using z table   

=  0.7486-0.0228

probability= 0.7258

B)

P(X< 7) = P[(X- ) / < (7-10.0) / 1.5 ]

= P(z < -2)

Using z table

= 0.0228

probability=0.0028

(C)

P(x >11 ) = 1 - P(x<11 )

= 1 - P[(x -) / < (11-10.0) /1.5 ]

= 1 - P(z <0.67 )

Using z table

= 1 - 0.7486

probability= 0.2514