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 10.8 minutes and a standard deviation of 1.9 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 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 = = 10.8

standard deviation = = 1.9

(a)

P(7 < x < 12) = P((7 - 10.8)/ 1.9) < (x - ) / < (12 - 10.8) / 1.9) )

= P(-2 < z < 0.63)

= P(z < 0.63) - P(z < -2)

= 0.7357 - 0.0228

= 0.7129

Probability = 0.7129

(b)

P(x < 7) = P((x - ) / < (7 - 10.8) / 1.9)

= P(z < -2)

Using standard normal table,

P(x < 7) = 0.0228

Probability = 0.0228

(c)

P(x > 12) = 1 - P(x < 12)

= 1 - P((x - ) / < (12 - 10.8) / 1.9)

= 1 - P(z < 0.63)

= 1 - 0.7357

= 0.2643

P(x > 12) = 0.2643

Probability = 0.2643