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 8.1 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

Answer 1

Answer:

a) 0.7898

b) 0.0516

c) 0.1587

Step-by-step explanation:

Given : Mean : $\mu=8.1\text{ minutes}$

Standard deviation : $\sigma =1.9\text{ minutes}$

Since , the police response time has a normal distribution.

The formula to calculate the z-score :-

$z=\dfrac{x-\mu}{\sigma}$

For x=5 minutes.

$z=\dfrac{5-8.1}{1.9}=-1.63$

For x=10 minutes.

$z=\dfrac{10-8.1}{1.9}=1$

a) The p-value =$P(-1.63<z<1)=P(z<1)-P(z<-1.63)$

$=0.8413447-0.0515507=0.789794\approx0.7898$

b) The p-value =$P(z<-1.63)=0.0515507\approx0.0516$

c) The p-value =$P(z>1)=1-P(z<1)$

$=1-0.8413447=0.1586553\approx0.1587$