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bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in less than 9 minutes. A management scientist has studied the service times and concluded that service times are exponentially distributed with a mean of 6 minutes. Determine what the bank means when it claims 'virtually all' its customers are served in under 9 minutes. Proportion of customers served in under 9 minutes

User Wellen
by
5.5k points

1 Answer

5 votes

Answer:

"0.7769" is the right approach. A further explanation is given below.

Explanation:

According to the question,

The parameter for the exponential distribution,

μ = 6

x = 9

Now,


P(X < 9) = 1 - exp ( (-x)/(\mu) )

On substituting the given values in the above equation, we get


= 1 - exp ((-9)/(6) )


=1-exp(-1.5)


=1-0.2231


=0.7769

User Stwilz
by
6.3k points
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