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 2.1 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

Explanation / Answer

mu= 9.7

sigma= 2.1

X= 10

Z=(X-mu)/sigma

=(10-9.7)/2.1

0.14285

probability =P(Z<0.1428)

=0.556798497

rounded answer is 0.5568

(b)

mu= 9.7

sigma= 2.1

X= 5

Z=(X-mu)/sigma

=(5-9.7)/2.1

-2.23809

probability =P(Z>-2.2380)

=0.987392577

rounded answer is 0.9874

(c)

mu= 9.7

sigma= 2.1

X= 15

Z=(X-mu)/sigma

2.52380

probability P1=P(Z<2.52381)

p1= 0.994195459

mu= 9.7

sigma= 2.1

X= 8

Z=(X-mu)/sigma

-0.80952

probability P2= p(Z<-0.80952)

0.2091069

Required probability is (P1-P2)=0.78508

rounded answer is 0.7851

..................

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