A local bank branch employs three tellers who can each help a customer on averag

Question

A local bank branch employs three tellers who can each help a customer on average in 6 minutes, with a standard deviation of 3 minutes. On average, 24 customers arrive at this bank per hour (in a random fashion). How long would customers have to wait if we do not pool the employees? (By "not pooling," we mean we have 3 separate lines forming; one in front of each of the 3 tellers. Assume that a person randomly enters one of the lines - each of the 3 lines takes one-third of the arrivals - and a person does not switch lines after entering a line.) Remember: any time you see the term "random" associated with the job arrivals it means the coefficient of variation is equal to one; that is, the standard deviation in the time between arrivals is equal to the mean time between arrivals.

1. Approximately 15 minutes

2. Approximately 0.07 minutes

3. Approximately 4.16 minutes

4. Approximately 12 minutes

Explanation / Answer

Ques: A local bank branch employs three tellers who can each help a customer on average in 6 minutes, with a standard deviation of 3 minutes. On average, 24 customers arrive at this bank per hour (in a random fashion). How long would customers have to wait if we do not pool the employees?

Ans: Approximately 15 minutes

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