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)/ 1.5) < (x - ) /  < (11 - 10) / 1.5) ]

= P(-2 < z < 0.67)

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

= 0.7258

Probability = 0.7258

(b)

P(x < 7) = P[(x - ) / < (7 - 10) / 1.5]

= P(z < -2)

= 0.0228

Probability = 0.0228

(c)

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

= 1 - P[(x - ) / < (11 - 10) / 1.5]

= 1 - P(z < 0.67)

= 0.2514

​​​​​​​Probability = 0.2514