Police response time to an emergency call is the difference between the time the
ID: 3329412 • 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 arrives at the scene. In a large city, it has been determined that the police response time follows a normal distribution with mean 8.2 minutes and standard deviation 1.7 minutes.
b. (2 points) What proportion of response times are less than 5 minutes? Use the z table and include your calculation of the z score. You may verify your answer with R or the Statistics Interactive App.
c. (2 points) What proportion of response times are between 5 and 10 minutes? Use the z table and include your calculation of the z score. You may verify your answer with R or the Statistics Interactive App.
d. (2 points) Longer response times can have extreme consequences. What time are 5% of response times are longer than?
Explanation / Answer
Mean is 8.2 and s is 1.7
z can be found as (x-mean)/s
1) P(x<5)=P(z<(5-8.2)/1.7)=P(z<-1.88) or 1-P(z<1.88), from normal distribution table we get 1-0.9699=0.0301
2) P(5<x<10)=P((5-8.2)/1.7<z<(10-8.2)/1.7)=P(-1.88<z<1.06)=P(z<1.06)-(1-P(z<1.88)) =0.8554-(1-0.9699)=0.8253
3) for the top 5% we can see that the z value for bottom 95% is given by normal distribution table by finding p=0.95 in the table and looking at the leftmost column and top most row for corresponding z value which is 1.65
thus, mean+s*Z=8.2+1.65*1.7=11.005