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 6.4 minutes and a standard deviation of 1.7 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 3 and 8 minutes

(b)

the response time is less than 3 minutes

(c)

the response time is more than 8 minutes

Answer 1

Solution :

Given that ,

mean = = 6.4 minutes

standard deviation = = 1.7 minutes

a) P( 3 < x < 8) = P[(3 - 6.4)/ 1.7) < (x - ) /  < (8 - 6.4) / 1.7) ]

= P( -2.00 < z < 0.94)

= P(z < 0.94) - P(z < -2.00)

Using z table,

= 0.8264 - 0.0228

= 0.8036

b) P(x < 3) = P[(x - ) / < (3 - 6.4) / 1.7 ]

= P(z < -2.00)

Using z table,

= 0.0228

c) P(x > 8) = 1 - P(x < 8)

= 1 - P((x - ) / < (8 - 6.4) / 1.7)

= 1 - P(z < 0.94)

= 1 - 0.8264

= 0.1736