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)
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?
So, the probability thsat delays will occur is 0.145
For the part 3), since by part 2), we know ...
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.