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 2.2 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

Given,

= 9.7 , = 2.2

We convert this to standard normal as

P(X < x) = P(Z < x - / )

a)

P(X < 10) = P(Z < 10 - 9.7 / 2.2)

= P( Z < 0.1364)

= 0.5542

b)

P( X > 5) = P( Z > 5 - 9.7 / 2.2)

= P (Z > -2.1364)

= P( Z < 2.1364)

= 0.9837

c)

P(8 < X < 15) = P( X < 15) - P(X < 8)

= P( Z < 15 - 9.7 / 2.2) - P( Z < 8 - 9.7 / 2.2)

= P(Z < 2.4091) - P(Z < -0.7727)

= 0.9920 - 0.2198

= 0.7722