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 10.0 minutes and a standard deviation of 1.5 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)

(a)

the response time is between 7 and 11 minutes

(b)

the response time is less than 7 minutes

(c)

the response time is more than 11 minutes

Answer 1

Solution :

Given that ,

mean = = 10.0

standard deviation = = 1.5

a) P(7 < x < 11) = P[(7 - 10.0)/ 1.5) < (x - ) /  < (11 - 10.0) / 1.5 ) ]

= P(-2.00 < z < 0.67)

= P(z < 0.67) - P(z < -2.00)

Using z table,

= 0.7486 - 0.0228

= 0.7258

b) P(x < 7)

= P[(x - ) / < (7 - 10.0) / 1.5 ]

= P(z < -2.00)

Using z table,

= 0.0228

c) P(x > 11 ) = 1 - p( x< 11)

=1- p P[(x - ) / < (11 - 10.0) / 1.5]

=1- P(z < 0.67)

= 1 - 0.7486

= 0.2514