Police response time to an emergency call is the difference between the time the
ID: 3220057 • Letter: P
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 8.6 minutes and a standard deviation of 1.7minutes. 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 10 minutes
(b) the response time is less than 5 minutes
(c) the response time is more than 10 minutes
Explanation / Answer
hrer for normal distribution z score =(X-mean)/std deviation
a) hence P(5<X<10)=P((5-8.6)/1.7<Z<(10-8.6)/1.7)=P(-2.1176<Z<0.8235)=0.7949-0.0171 =0.7778
b)P(X<5)=P(Z<-2.1176)=0.0171
c)P(X>10)=1-P(Z<0.8235)=1-0.7949=0.2051