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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

Respuesta :

Cricetus

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,

⇒  [tex]P(X < 9) = 1 - exp ( \frac{-x}{\mu} )[/tex]

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

⇒                  [tex]= 1 - exp (\frac{-9}{6} )[/tex]

⇒                  [tex]=1-exp(-1.5)[/tex]

⇒                  [tex]=1-0.2231[/tex]

⇒                  [tex]=0.7769[/tex]

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