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
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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