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 8.3 minutes and a standard deviation of 1.6 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 5 and 10 minutes


(b) the response time is less than 5 minutes


(c) the response time is more than 10 minutes

Answer 1

Solution :

Given that,

mean = = 8.3

standard deviation = = 1.6

a ) P (5 < x < 10 )

P ( 5 - 8.3 / 1.6) < ( x -  / ) < ( 10 - 8.3 / 1.6)

P ( - 3.3 / 1.6 < z < 1.7 / 1.6 )

P (-2.06 < z < 1.06 )

P ( z < 1.06 ) - P ( z < -2.06)

Using z table

= 0.8554 - 0.0197

= 0.8357

Probability = 0.8357

b ) P( x < 5 )

P ( x - / ) < ( 5 - 8.3 / 1.6 )

P ( z < -3.3 / 1.6 )

P ( z < -2.06)

= 0.0197

Probability = 0.0197

c ) P (x > 10 )

= 1 - P (x < 10 )

= 1 - P ( x -  / ) < ( 10 - 8.3 / 1.6)

= 1 - P ( z <1.7 / 1.6 )

= 1 - P ( z < 1.06 )

Using z table

= 1 - 0.8554

= 0.1446

Probability =0.1446