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 9.9 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 :

(a)

P(x < 10) = P[(x - ) / < (10 - 9.9) / 2.4]

= P(z < 0.04)

= 0.516

(b)

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

= 1 - P[(x - ) / < (5 - 9.9) /2.4 ]  

= 1 - P(z < -2.04)

= 0.0207

(c)

P(8 < x < 15) = P[(8 - 9.9)/ 2.4) < (x - ) /  < (15 - 9.9) / 2.4) ]

= P(-0.79 < z < 2.125)

= P(z < 2.125) - P(z < -0.79)

= 0.7684