A bank wishing to increase its customer base advertises that it has the fastest

Question

A 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 11 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 11 minutes.
Hint: An exponentially distributed random variable has a probability density function of the form ke^?kx for x?0and is 0 otherwise. The mean of an exponentially-distributed random variable is 1/k.

Proportion of customers served in under 11 minutes =

Explanation / Answer

mean = 1/k

so, k = 1/6

P(t<11) =1 - ke^-kx

= 1- (1/6 * e^(-11/6))

= 0.973

So, Proportion of customers served in under 11 minutes = 0.973

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