Question

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.5 minutes and a standard deviation of 2.4 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes


(b) longer than 5 minutes


(c) between 8 and 15 minutes

Answer 1

Solution :

Given that,

mean = = 8.5

standard deviation = =2.4

A ) P( x <10)

P ( x - / ) < ( 10- 8.5/ 2.4 )

P ( z < 1.5 / 2.4 )

P ( z < 0.62)

= 0.7324

Probability = 0.7324

B ) P (x > 5 )

= 1 - P (x < 5 )

= 1 - P ( x -  / ) < ( 5 - 8.5/ 2.4)

= 1 - P ( z <-3.5 / 2.4)

= 1 - P ( z < -1.46 )

Using z table

= 1 - 0.0721

= 0.9279

Probability = 0.9279

C ) P ( 8 < x < 15 )

P ( 8 - 8.5/ 2.4) < ( x -  / ) < ( 15 - 8.5/ 2.4)

P (0.5 / 2.4 < z < 6.5 / 2.4 )

P (0.21 < z < 2.71 )

P ( z < 2.71 ) - P ( z < 0.21)

Using z table

= 0.9966 - 0.5832

= 0.4135

Probability = 0.4135