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Probability

Please see attached files for question. I can't seem to get the answer for PART3.

(See attached file for full problem description with equations)

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A bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up window occur at random, with a mean arrival rate of 24 customers per hour or 0.4 customers per minute.

1) What is the mean or expected number of customers that will arrive in a five minute period?
Denote by the number of customers in the i-th minute. So, . Hence,

2) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the mean arrival rate in part 1 and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.

By part 1), we know that the mean or expected number of customers that will arrive in a five minute period is 2. So, . Denote by X the number of customers will arrive during a five-minute period.

3) Delays are expected if more than three customers arrive during any five-minute period. What is the probability thsat delays will occur?

P(X>3)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)
=1-
So, the probability thsat delays will occur is 0.145
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For the part 3), since by part 2), we know ...

Solution Summary

The solution clearly explains the steps required to get to the answer. The steps are explained in a very easy to understand manner and can be easily followed along by anyone with a basic understanding of probability. Overall, an excellent response to the question being asked.

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