10. Branch banks must keep enough money on hand to satisfy customers’ cash dem:
Suppose that the daily demand for cash at a
anch of University Bank follows a logno
distribution with means and standard deviation summarized as follows (in $1,000s):
Mondsy Tuesday Wednesday Thursday Friday _Ssturday Sunday
Mean S XXXXXXXXXXS60 s120 S10 $65
StdDev $26 S18 $13 ss sug gn Suslg
‘An armored truck delivers cash to this bank once a week. The manager of the bank can orde
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 bal-
ance throughout the week.
. 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 a the start each week to ensure there is at most a 0.10%
chance of running out of money?
12.10
Use the same Random Variables from the 12.5 example. You can use events 1 through 7 to simulate the
cash demands on Monday through Sunday. Run a simulation model over 100 iterations. Use the same.
Mean and StDev as in the book, but assume cash demands follow a normal distribution.
Set up the model as specified in part a, and calculate the probability that the bank will run out of money
asin part b. Itis simplest to set the model up to calculate the cash remaining at the end of the week,
after demands have occu
ed for all 7 days. Then, program an if{) function to check if the remaining cash
is<0.
For part c. what is the amount of money needed at the start of the week to ensure there is at most a 5%
chance of running out of money?
5. A debate recently erupted about the pptimal strategy for playing a game on the TV show
called “Lets Make a Deal” In one of the games on this show, the contestant would be given
of prizes behind three closed doors. A valuable prize was behind one door and
oes were behind the other two doors “After the contestant selected 2 doo
P14 open one o the two remaining door ib Teveal one of the worthless prizes.
fore opening the selected door, th Bose vould give the contestant the opportunity
Op er selection tothe other door that had ot been opened. The question is.
the contestant switch?
estat is allowed to play tis game 500 tne, always picks door number L
witches when given the option. If he valuable prize is equally likely to be
ehind each door at the beginning of each play, how many times would the contestant win
Hn ile prise? Use simulation 0 answer this question.
Nw suppose the contestants allowed to Py is game another 500 times. This time the
ys selects door number 1 initaly and ilches when given the option. Using
ton, how many ties would th contest win the valuable prize!
you wer contestant on this shows what ocd you do if given the option of swiching
doors?
ot olarship endowments for a major public university.
dowments fof © 70 e awarded from