# Averages and Probability

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The Wizard Tax Service is analyzing its operations during the month prior to the April 15 tax filing date. There is currently only one tax preparer at Wizard. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with and average time between arrivals of 12 minutes. When the tax return is being completed, the customer is at the tax preparer's desk working with the preparer and this is considered the service time. The time to complete a return for a customer is exponentially distributed with a mean time of 10 minutes. Customers are processed in the order of arrival. Based on this information:

A. On average and measured from when a customer arrives at Wizard, how much time does the customer spend at the tax service having his tax return completed?

B. What is the average number of customers at the tax service, whether waiting for the tax preparer or having the return prepared?

C. An arriving customer will not wait if there are at least three others waiting for the tax preparer. What is the probability that the arriving customer will not wait?

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##### Solution Summary

The averages and probability are examined. The expert determines how much time does the customer spend at tax services to have his taxes completed.

##### Solution Preview

Arrival rate per hour: λ=(60/12)/hour=5/hour

Service rate: µ=1/(10/60)=6/hour, ...

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