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

Solution :

Given that ,

mean = = 7.6

standard deviation = = 2.3

a) P(3 < x < 9) = P[(3 - 7.6)/ 2.3) < (x - ) /  < (9 - 7.6) / 2.3) ]

= P(-2.00 < z < 0.61)

= P(z < 0.61) - P(z < -2.00)

Using z table,

= 0.7291 - 0.0228

= 0.7063

b) P(x < 3) = P[(x - ) / < (3 - 7.6) /2.3 ]

= P(z < -2.00)

Using z table,

= 0.0228

c) P(x > 9) = 1 - p( x< 9)

=1- p P[(x - ) / < (9 - 7.6) /2.3 ]

=1- P(z < 0.61)

Using z table,

= 1 - 0.7291

= 0.2709