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 9.7 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 = = 9.7

standard deviation = = 2.4

(a)

P(x < 10) = P[(x - ) / < (10 - 9.7) / 2.4]

= P(z < 0.125)

= 0.5497

Probability = 0.5497

(b)

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

= 1 - P[(x - ) / < (5 - 9.7) /2.4 ]

= 1 - P(z < -1.9583)

= 1 - 0.0251

= 0.9749

Probability = 0.9749

(c)

P(8 < x < 15) = P[(8 - 9.7)/ 2.4) < (x - ) /  < (15 - 9.7) /2.4 ) ]

= P(-0.7083 < z < 2.2083)

= P(z < 2.2083) - P(z < -0.7083)

= 0.9864 - 0.2394

= 0.7470

Probability = 0.7470