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 6.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, find the following probabilities.
a) between 5 and 10 min.
b) less than 5 min.
c) more than 10 min.

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raphealnwobi raphealnwobi · Answer 1 · 2022-03-09T09:31:02+01:00

The probability that a randomly received emergency call is between 5 and 10 min is 77.97%.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation and x is the raw score.

Given that μ = 6.4, σ = 1.7

For x = 5:

z = (5 - 6.4) / 1.7 = -0.83

For x = 10:

z = (10 - 6.4) / 1.7 = 2.12

a) P(5 < x < 10) = P(-0.83 < z < 2.12) = P(z < 2.12) - P(z < -0.83) = 0.9830 - 0.2033 = 0.7797

b) P( x < 5) = P(z < -0.83) = 0.2033

c) P(x > 10) =1 - P(z < 2.12) = 1 - 0.9830 - 0.2033 = 0.017

The probability that a randomly received emergency call is between 5 and 10 min is 77.97%.

Find out more on Z score at: https://brainly.com/question/25638875