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 10.4 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.). (PLEASE SHOW WORK!! :) )

(a) the response time is between 7 and 12 minutes


(b) the response time is less than 7 minutes

(c) the response time is more than 12 minutes

Answer 1

Solution:

Given that,

mean =   = 10.4 minutes

standard deviation =   = 1.7 minutes

A ) P ( 7 < x < 12 )

P ( 7 - 10.4 / 1.7) < ( x -  / ) < ( 12 - 10.4 / 1.7)

P ( - 3. 4 / 1.7 < z < 1.6 / 1.7 )

P (- 2 < z < 0. 94 )

P (z < 0.94 ) - p ( z < - 2 )

Using z table

= 0.8264 - 0.0228

= 0.8036

Probability = 0.8036

B ) P ( x < 7 )

P ( x -  / ) < ( 7 - 10.4 / 1.7)

P ( z < -3.4 / 1.7 )

P ( z < - 2 )

Using z table

= 0.0228

Probability = 0.0228

C ) P ( x > 12 )

= 1 - P ( x < 12 )

= 1- P ( x -  / ) < ( 12 - 10.4 / 1.7)

= 1- P ( z < 1.6 / 1.7 )

= 1- P ( z < 0.94 )

Using z table

= 1 - 0.8264

= 0.1736

Probability =  0.1736