# bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in

Question

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

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1 year 2021-09-04T15:44:48+00:00 1 Answers 12 views 0

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

Step-by-step explanation:

According to the question,

The parameter for the exponential distribution,

μ = 6

x = 9

Now,

⇒  $$P(X < 9) = 1 – exp ( \frac{-x}{\mu} )$$

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

⇒                  $$= 1 – exp (\frac{-9}{6} )$$

⇒                  $$=1-exp(-1.5)$$

⇒                  $$=1-0.2231$$

⇒                  $$=0.7769$$