College stat

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 1.4 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

Answer 1

Obtain a z-score chart

http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

 

(a)

z₅ = (5 - 8) / 1.4

z₅ = -3 / 1.4

z₅ = -2.14

z₁₀ = (10 - 8) / 1.4

z₁₀ = 2 /1.4

z₁₀ = 1.42

What is the area between -2.14 and 1.42?

 

(b)

What is the area below -2.14?

 

(c)

What is the area above 1.42>