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 9.6 minutes and a standard deviation of 2.3 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 11 minutes (b) the response time is less than 5 minutes (c) the response time is more than 11 minutes

Answer 1

Answer:

a) 0.7063; b) 0.0228; c) 0.2709

Step-by-step explanation:

We use z scores for these problems.  The formula for a z sore is

$z=\frac{X-\mu}{\sigma}$

For part a,

We want P(5 ≤ X ≤ 11):

z = (5-9.6)/2.3 = -4.6/2.3 = -2

z = (11-9.6)/2.3 = 1.4/2.3 = 0.61

The area under the curve to the left of z = -2 is 0.0228.  The area under the curve to the left of z = 0.61 is 0.7291.  This makes the area between them

0.7291 - 0.0228 = 0.7063

For part b,

We want P(X ≤ 5):

z = (5-9.6)/2.3 = -4.6/2.3 = -2

The area under the curve to the left of z = -2 is 0.0228.

For part c,

We want P(X > 11):

z = (11-9.6)/2.3 = 1.4/2.3 = 0.61

The area under the curve to the left of z = 0.61 is 0.7291.  However, we want the area to the right; this means we subtract from 1:

1-0.7291 = 0.2709