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Law Enforcement: Police Response Time Police response time to an emergency call

ID: 3062933 • Letter: L

Question

Law Enforcement: Police Response Time 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 (based on information from The Denver Post). Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, what is the probability that the response time will be (ROUND ANSWERS TO 4 DECIMAL PLACES X.XXXX) (a) exactly 5 minutes? (b) less than 5 minutes? (c) more than 10 minutes? (d) between 5 and 10 minutes? (e) either less than 5 or more than 10 minutes?

Explanation / Answer

a) P(X = 5) = 0

b) P(x < 5)

= P(z < (5 - 8.4)/1.7)

= P(z < -2)

= 0.0228

c) P(X > 10)

= P(z > (10 - 8.4)/1.7)

= P(z > 0.94)

= 0.1733

d) P(5 < X < 10)

= 1 - (0.0228 + 0.1733)

= 0.8039

e) P(X < 5 or X > 10)

= 0.0228 + 0.1733

= 0.1961