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 7.2 minutes and a standard deviation of 2.1 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)

(a) the response time is between 3 and 9 minutes

(b) the response time is less than 3 minutes

(c) the response time is more than 9 minutes

Answer 1

µ = 7.2, σ = 2.1

a) P(3 < X < 9) =

= P( (3-7.2)/2.1 < (X-µ)/σ < (9-7.2)/2.1 )

= P(-2 < z < 0.8571)

= P(z < 0.8571) - P(z < -2)

Using excel function:

= NORM.S.DIST(0.8571, 1) - NORM.S.DIST(-2, 1)

= 0.7816

b) P(X < 3) =

= P( (X-µ)/σ < (3-7.2)/2.1 )

= P(z < -2)

Using excel function:

= NORM.S.DIST(-2, 1)

= 0.0228

c) P(X > 9) =

= P( (X-µ)/σ > (9-7.2)/2.1)

= P(z > 0.8571)

= 1 - P(z < 0.8571)

Using excel function:

= 1 - NORM.S.DIST(0.8571, 1)

= 0.1957