Question

# Police response time to an emergency call is the difference between the time the call is...

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. (Round your answers to four decimal places.)

(a) the response time is between 3 and 8 minutes

(b) the response time is less than 3 minutes

(c) the response time is more than 8 minutes

Solution :

Given that ,

mean = = 6.4

standard deviation = = 1.7

(a)

P(3 < x < 8) = P[(3 - 6.4)/ 1.7) < (x - ) /  < (8 - 6.4) / 1.7) ]

= P(-2 < z < 0.94)

= P(z < 0.94) - P(z < -2)

= 0.8264 - 0.0228

= 0.8036

Probability = 0.8036

(b)

P(x < 3) = P[(x - ) / < (3 - 6.4) / 1.7]

= P(z < -2)

= 0.0228

Probability = 0.0228

(c)

P(x > 8) = 1 - P(x < 8)

= 1 - P[(x - ) / < (8 - 6.4) / 1.7]

= 1 - P(z < 0.94)

= 1 - 0.8264

= 0.1736

Probability = 0.8264

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