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 10.4 minutes and a standard deviation of 1.7 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 12 minutes (b) the response time is less than 7 minutes (c) the response time is more than 12 minutes

Answer 1

Solution :

Given that ,

mean = = 10.4

standard deviation = = 1.7

a) P(7 < x < 12) = P[(7 - 10.4)/ 1.7) < (x - ) /  < (12 - 10.4) /1.7 ) ]

= P( -2 < z < 0.94)

= P(z < 0.94) - P(z < -2 )

Using z table,

= 0.8264 - 0.0228

= 0.8036

b) P(x < 7) = P[(x - ) / < (7 - 10.4) / 1.7]

= P(z < -2)

Using z table,

= 0.0228

c) P(x > 12) = 1 - p( x< 12)

=1- p P[(x - ) / < (12 - 10.4) /1.7 ]

=1- P(z < 0.94)

Using z table,

= 1 - 0.8264

= 0.1736