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 $$1,000$ s$)$:

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. Of course, keeping excessive cash reserves

would guard against this happenstance. However, cash is a non$-$interest 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?