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 2.7 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 = = 9.9

standard deviation = = 2.7

(a)

P(x < 10) = P((x - ) / < (10 - 9.9) / 2.7) = P(z < 0.037)

Using standard normal table,

P(x < 10) = 0.5148

Probability = 0.5148

b)

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

= 1 - P((x - ) / < (5 - 9.9) / 2.7)

= 1 - P(z < -1.8148)   Using standard normal table,

= 1 - 0.0348

= 0.9652

P(x > 5) = 0.9652

Probability = 0.9652

c)

P(8 < x < 15) = P((8 - 9.9 / 2.7) < (x - ) / < (15 - 9.9) / 2.7) )

P(8 < x < 15) = P(-0.7037 < z < 0.189)

P(8 < x < 15) = P(z < 0.189) - P(z < -0.7037)

Probability = 0.5750 - 0.2408 = 0.3342