Branch banks must keep enough money on hand to satisfy customers' cash demands. Suppose that the daily

Question:

Branch banks must keep enough money on hand to satisfy customers' cash demands. Suppose that the daily demand for cash at a branch of University Bank follows a lognormal distribution with means and standard deviation summarized as follows (in $1,000s):

An armored truck delivers cash to this bank once a week. The manager of the bank can order any amount of cash she desires for this delivery. Of course, running out of cash in any week is very undesirable as customers of the bank expect to be able to withdraw their deposits on demand. Keeping excessive cash reserves would guard against this happenstance. However, cash is a noninterest earning asset, so there is an opportunity cost for holding excess cash reserves.
a. Suppose the bank manager follows the practice of ordering enough cash to start each week with a balance of $825,000. Create a spreadsheet model to track the daily cash balance throughout the week.
b. What is the probability that the bank will run out of money at some point during the week?
c. What amount of money is needed at the start each week to ensure there is at most a 0.10% chance of running out of money?

Distribution
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