Police response time to an emergency call is the difference

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

Solution

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