The Customer Service Center in a large New York department store has determined

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 2.6 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

Explanation / Answer

Mu=9.7 S=2.6

A)z=X-Mu/S

=10-9.7/2.6

=0.115

P(X<10)

P(z<0.115)

=0.0438+0.5

=0.5438. Or 54.37%

B)z=5-9.7/2.6

Z=-1.81

P(X>5)

=P(z>-1.81)

=0.4689+0.5

=0.9689. Or 96.89%

C)

X1=8. X2=15

Z1=X1-Mu/S

=8-9.7/2.6

=-0.653

Z2=X2-Mu/S

=15-9.7/2.6

=2.04

P(8<X<15)

P(-0.653<z<2.04)

=0.2422+0.4793

=0.7215. Or 72.15%

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