Question

3. 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 10 minutes and a standard deviation of 2.2 minutes. For a randomly received emergency call, what is the probability that the response time will be a) between 5 and 10 minutes? b) More than 5 minutes? c) Less than 15 minutes? d) What is the response time in minutes at the 80th percentile?

Answer 1

(a)

= 10

= 2.2

To find P(5 <X < 10):

Z = (5 - 10)/2.2

= - 2.2727

Table gives area= 0.4884

So,

Answer is:

0.4884

(b)

To find P(X>5):

Z = (5 - 10)/2.2

= - 2.2727

Table gives area= 0.4884

So,

P(X>5) = 0.5 + 0.4884 = 0.9884

So,

Answer is:

0.9884

(c)

To find P(X<15):

Z= (15- 10)/2.2

= 2.2727

Table gives area= 0.4884

So,

P(X<15) = 0.5 - 0.4884 = 0.0116

So,

Answer is:

0.0116

(d)

80th percentile corresponds to area = 0.80 - 0.50 = 0.30 from mid value to Z on RHS

Table gives Z= 0.84

So,

Z= 0.84 = (X- 10)/2.2

So,

X = 10 + (0.84 X 2.2) = 11.848

So,

Answer is:

11.848