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 8.9 minutes and a standard deviation of 2.8 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 = = 8.9

standard deviation = = 2.8

(a)

P(x < 10) = P[(x - ) / < (10 - 8.9) /2.8 ]

= P(z < 0.39)

= 0.6517

Probability = 0.6517

(b)

P(x > 5) = 1 - P(x < 5)

= 1 - P[(x - ) / < (5 - 8.9) / 2.8]

= 1 - P(z < -1.39)

= 1 - 0.0823

= 0.9177

Probability = 0.9177

(c)

P(8 < x < 15) = P[(8 - 8.9)/ 2.8) < (x - ) /  < (15 - 8.9) / 2.8) ]

= P(-0.32 < z < 2.18)

= P(z < 2.18) - P(z < -0.32)

= 0.9854 - 0.3745

= 0.6109

Probability = 0.6109