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

standard deviation = = 15

a ) P (3 < x < 8 )

P ( 3 - 6.4 / 1.7) < ( x -  / ) < ( 8 - 6.4 / 1.7)

P ( - 3.4 /1.7 < z < 1.6 / 1.7 )

P (-2 < z <0.94 )

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

Using z table

= 0.8264 - 0.0228

= 0.8036

Probability =0.8036

b ) P( x < 3)

P ( x - / ) < ( 3 - 6.4 / 1.7)

P ( z < -3.4 / 1.7 )

P ( z < - 2)

= 0.0228

Probability = 0.0228

c ) P (x > 8)

= 1 - P (x < 8 )

= 1 - P ( x -  / ) < ( 8 - 6.4 / 1.7)

= 1 - P ( z < 1.6 / 1.7 )

= 1 - P ( z < 0.94)

Using z table

= 1 - 0.8264

= 0.1736

Probability = 0.1736