Problem $10-22($Algo$)$

You are planning employees for a bank. You plan for $6$ tellers. Tellers take $12$ minutes per customer, with a standard deviation of $6$

minutes. Customers will arrive one every $3$ minutes according to an exponential distribution $($recall that the standard deviation is equal

to the mean$).$ Every customer who arrives eventually gets serviced. Use waiting line approximation to answer the following questions.

a$.$ On average, how many customers would be waiting in line?

Note: Round your intermediate calculations to $4$ decimal places and final answer to $3$ decimal places.

Number of customers

b$.$ On average, how long would a customer spend in the bank?

Note: Round your intermediate calculations to $4$ decimal places and final answer to $3$ decimal places.

Time spent by a customer

minutes

You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times.

c$.$ If a customer arrived, saw the line, and decided not to get in line, that customer has

reneged

quit

refused

balked

evaded

d$.$ A customer who enters the line but decides to leave the line before getting service is said to have

quit

exited

balked

reneged

escaped