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 9.3 minutes and a standard deviation of 2.5 minutes.

1) What is the probability that for a randomly chosen customer with a complaint the amount of time spent resolving the complaint will be less than 12 minutes? Write your answer to four decimal places.

2)  What is the probability it will be more than five minutes? Write your answer to four decimal places.

3) What is the probability the amount of time will be between 5 and 12 minutes? Write your answer to four decimal places

Answer 1

Solution :

Given that ,

mean = = 9.3

standard deviation = = 2.5

1) P(x < 12) = P[(x - ) / < (12 - 9.3)/2.5 ]

= P(z < 1.08)

= 0.8599

Probability = 0.8599

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

= 1 - P[(x - ) / < (5 - 9.3) /2.5 )

= 1 - P(z < -1.72)

= 1 - 0.0427

0.9573

Probability = 0.9573

3) P(5 < x < 12) = P[(5 - 9.3)/ 2.5) < (x - ) /  < (12 - 9.3) / 2.5) ]

= P(-1.72 < z < 1.08)

= P(z < 1.08) - P(z < -1.72)

= 0.8599 - 0.0427

0.8172

Probability = 0.8172