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

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

Mean is 8.4 and s is 1.7. z is given as (x-mean)/s

a) P(x=5)=0 because point probability is 0 for normal distribution

b) P(x<5)=P(z<(5-8.4)/1.7)=P(z<-2) or 1-P(z<2), from normal distribution table we get 1-0.9772=0.0228

c) P(x>10)=P(z>(10-8.4)/1.7)=P(z>0.94) or 1-P(z<0.94) , from normal distribution table we get 1-0.8264=0.1736

d) P(5<x<10)=P(x<10)-P(x<5)= 0.8264-0.0228=0.8036 (from part b) and c))

e) 1-P(5<x<10)=1-0.8036 =0.1964

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