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umka2103 [35]
3 years ago
7

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th

e 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
Mathematics
1 answer:
DerKrebs [107]3 years ago
7 0

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

=0.8413447-0.0515507=0.789794\approx0.7898

b) The p-value =P(z

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

=1-0.8413447=0.1586553\approx0.1587

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