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

Answer 1

"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`