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 11.2 minutes and a standard deviation of 2.1 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

a)

Let X : police response time is normally distributed with mean = 11.2 and standard deviation = 2.1

We asked P( 7 < X < 13) = P[7-/ < X -/ < 13-/ ]

=P[(7-11.2)/2.1 < Z < (13 - 11.2)/2.1]

=P( -2 < Z < 0.86)

= P ( Z < 0.86 ) - P( Z < -2)

= 0.8051 - 0.0228

P( 7 < X < 13 ) = 0.7823

b) P( X < 7 ) = P [ X - / < 7 - 11.2/2.1]

P( X < 7 ) = P( Z < -2)

P( X < 7 ) = 0.0228

c) P( X > 13 ) = P[ X - / > 13 - 11.2/2.1]

P( X > 13) = P( Z > 0.86)

= 1 - P( Z < 0.86)

P( X > 13 ) = 1 - 0.8051

P( X > 13) = 0.1949