Police response time to an emergency call is the difference between the time the
ID: 3131189 • 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 8.6 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 5 and 10 minutes
(b) the response time is less than 5 minutes
(c) the response time is more than 10 minutes
Explanation / Answer
mean = 8.6
standard deviation = 1.9
a)p(5<x<10) =
For x = 5 , z = (5 - 8.6) / 1.9 = -1.89 and for x = 10, z = (10 - 8.6) / 1.9 = 0.73
Hence P(5 < x < 10) = P(-1.89 < z < 0.73) = [area to the left of z = 0.73] - [area to the left of -1.89]
= 0.7673 - 0.0294 = 0.0.7379
b) p(x<5)
For x = 5, the z-value z = (5 - 8.6) / 1.9 = -1.89
Hence P(x < 5) = P(z < -1.89) = [area to the left of -1.89] = 0.0294
c) p(x>10) =
For x = 10, z = (10 - 8.6) / 1.9 = 0.73
Hence P(x > 10) = P(z > 0.73) = [total area] - [area to the left of 0.73]
= 1 - 0.7673 = 0.2327