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 7.6 minutes and a standard deviation of 2.3 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.) (a) the response time is between 3 and 9 minutes (b) the response time is less than 3 minutes (c) the response time is more than 9 minutes

Answer 1

(a)

= 7.6

= 2.3

To find P(3 < X <9):

Case1; For X from 3 to mid value:

Z = (3 - 7.6)/2.3 = - 2.00

Table of Area Under Standard Normal Curve gives area = 0.4772

Case2: For X from mid value to 9:

Z = (9 - 7.6)/2.3 = 0.61

Table of Area Under Standard Normal Curve gives area = 0.2291

So,

P(3 < X< 9) = 0.4772+ 0.2291 = 0.7063

So,

Answer is:

0.7063

(b)

To find P(X<3):

Z = (3 - 7.6)/2.3 = - 2.00

Table of Area Under Standard Normal Curve gives area = 0.4772

So,

P(X<3) = 0.5 - 0.4772 = 0.0228

So,

Answer is:

0.0228

(c) To find P(X>9):

Z = (9 - 7.6)/2.3 = 0.61

Table of Area Under Standard Normal Curve gives area = 0.2291

So,

P(X>9) = 0.5 - 0.2291 = 0.2709

So,

Answer is:

0.2709