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

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JeanaShupp JeanaShupp · Answer 1 · 2019-07-10T08:38:19+02:00

Answer:

a) 0.7898

b) 0.0516

c) 0.1587

Step-by-step explanation:

Given : Mean : [tex]\mu=8.1\text{ minutes}[/tex]

Standard deviation : [tex]\sigma =1.9\text{ minutes}[/tex]

Since , the police response time has a normal distribution.

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=5 minutes.

[tex]z=\dfrac{5-8.1}{1.9}=-1.63[/tex]

For x=10 minutes.

[tex]z=\dfrac{10-8.1}{1.9}=1[/tex]

a) The p-value =[tex]P(-1.63<z<1)=P(z<1)-P(z<-1.63)[/tex]

[tex]=0.8413447-0.0515507=0.789794\approx0.7898[/tex]

b) The p-value =[tex]P(z<-1.63)=0.0515507\approx0.0516[/tex]

c) The p-value =[tex]P(z>1)=1-P(z<1)[/tex]

[tex]=1-0.8413447=0.1586553\approx0.1587[/tex]