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 11.6 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 7 and 13 minutes

(b) the response time is less than 7 minutes

(c) the response time is more than 13 minutes

Answer 1

TOPIC:Normal distribution.

→ Let ue dedine, x = The police response time (in minutes n so, / X ~ N(M = 11:6, 8 = 2.31 7 X- P 13 > -11.6 2.3 -11-6 2.3 @ We need, P ( 7 (x413). PP (?-16 (Kode ( 13-16) 72= =P(-2 (Z < 0.608? [ 201= 0of of 2 - (0.608? – 9(-2). [x: 27-2) = -0);) = q (0.6088) - {1 - 0(23. NNlod] (From Normal table values, = 0.7286 - 31-O. 2 (0.7058) come

by we need, *P(x<7). - ? (*<?="0). =P ( 2 (-2. 7-11.6 2.3 D(-2). = 1- 2 (2). (From Normal = 1-0. 9772. = 10.0228 (Ans cy we need, p(xY13). -1 (RM 139 =P (2 y 0.6087). = - (0.6087). from Normal) table values al 2 0.7286. 10. 2714 (Ang).