Statistics and Probability Question

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 2.1 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

This is a problem that requires usage of the standard normal curve table or a calculator that calculates the cumulative normal distribution

a) Less than 10 minutes

Pr ( x < 10 minutes ) = Pr [ z < ( 10-9.7)/2.1) ] = Pr ( z < .1428 ) = .5568

b) Longer than 5 minutes

Pr ( x > 5 ) = Pr [ z > ( 5 - 9.7 ) /2.1 ) ] = Pr ( z > -2.38 ) = .9874

c) between 8 and 15 minutes

Pr ( 8 <x <15 ) = Pr [ ( 8 - 9.7 ) / 2.1 < z < ( 15 - 9.7 ) / 2.1 ) ] = Pr ( -.810< z < 2.52 ) = .785