### Due to recent increase in business law firm secretary

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Due to a recent increase in business, a law firm secretary must now? word-process an average of 20 letters a day? (assume a Poisson distribution). It takes him approximately 20 minutes to type each letter? (assume an exponential distribution). Assume the secretary works 8 hours a day.

?a) The? secretary's utilization rate is .833 (round your response to three decimal? places).

?b) The average waiting time before the secretary word-processes a letter is 1.663 hours ?(round your response to three decimal places).

?c) The average number of letters waiting to be done is 4.166 letters ?(round your response to three decimal places).

?d) The probability that the secretary has more than 5 letters to do is _________?(round your response to three decimal places).

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