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

Please show how to solve

Answer 1

µ = 9.6, σ = 2.3

a) P(5 < X < 11) =
= P( (5-9.6)/2.3 < (X-µ)/σ < (11-9.6)/2.3 )
= P(-2 < z < 0.6087)
= P(z < 0.6087) - P(z < -2)
Using excel function:
= NORM.S.DIST(0.6087, 1) - NORM.S.DIST(-2, 1)
= 0.7059

b) P(X < 5) =
= P( (X-µ)/σ < (5-9.6)/2.3 )
= P(z < -2)
Using excel function:
= NORM.S.DIST(-2, 1)
= 0.0228

c) P(X > 11) =
= P( (X-µ)/σ > (11-9.6)/2.3)
= P(z > 0.6087)
= 1 - P(z < 0.6087)
Using excel function:
= 1 - NORM.S.DIST(0.6087, 1)
= 0.2714