Police response time to an emergency call is the difference between the time the
ID: 3386874 • 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 8.3 minutes and a standard deviation of 2.0 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
Normal Distribution
Mean ( u ) =8.3
Standard Deviation ( sd )=2
Normal Distribution = Z= X- u / sd ~ N(0,1)
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 5) = (5-8.3)/2
= -3.3/2 = -1.65
= P ( Z <-1.65) From Standard Normal Table
= 0.04947
P(X < 10) = (10-8.3)/2
= 1.7/2 = 0.85
= P ( Z <0.85) From Standard Normal Table
= 0.80234
P(5 < X < 10) = 0.80234-0.04947 = 0.7529
b)
P(X < 5) = (5-8.3)/2
= -3.3/2= -1.65
= P ( Z <-1.65) From Standard Normal Table
= 0.0495
c)
P(X > 10) = (10-8.3)/2
= 1.7/2 = 0.85
= P ( Z >0.85) From Standard Normal Table
= 0.1977