Police Statistics Problem

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 7.2 minutes and a standard deviation of 2.1 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 9 minutes 

 

(b) the response time is less than 3 minutes 

 

(c) the response time is more than 9 minutes 

Answer 1

(b) Prob( x<3) = Prob( z < (3-7.2)/2.1) = Prob ( z < -2) = 0.02275 = 2.275%

(a) Prob( 3 < x < 9) = Prob ( x<9) - prob(x < 3)

Prob(x < 9) = Prob ( z < (9-7.2)/2.1) = Prob ( z < 1.8/2.1) = Prob( z < 6/7) = 0.804317 = 80.4317%

The probability is 80.4317% - 2.275% <--- from part (b)

= 78.1567%

(c) Prob(x>9) = 1 - Prob(x<9) = 100% - 80.4317% = 19.5683%