Police response time to an emergency call is the difference between the time the
ID: 3367138 • Letter: P
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 8.0 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 5 and 9 minutes
(b) the response time is less than 5 minutes
(c) the response time is more than 9 minutes
Explanation / Answer
Mean = 8 minutes
Standard deviation = 1.5 minutes
P(X < A) = P(Z < (A - mean)/standard deviation)
a) P(5 < X < 9) = P(X < 9) - P(X < 5)
= P(Z < (9 - 8)/1.5) - P(Z < (5 - 8)/1.5)
= P(Z < 0.67) - P(Z < -2)
= 0.7486 - 0.0228
= 0.7258
b) P(X < 5) = P(Z < -2)
= 0.0228
c) P(X > 9 minutes) = 1 - P(X < 9)
= 1 - P(Z < 0.67)
= 1 - 0.7486
= 0.2514