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

Answer:

"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

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

⇒                  $=1-exp(-1.5)$

⇒                  $=1-0.2231$

⇒                  $=0.7769$