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Normal Distribution Question

Joined
Mar 28, 2012
Messages
1
Hi,

Can anyone please assist with the following:
Robert operates a currency exchange office at an airport. His office is open at night when the airport bank is closed and he makes most of his profit on returning American tourists who need to exchange their remaining currency back into US dollars. From experience, Robert knows that the demand for dollars on any night is normally distributed with a mean m $15,000 and a standard deviation of s $1,000.
If Robert carries too much money overnight, he has to pay interest on the cash. On the other hand, if he runs out of US dollars he has to forgo possble profit. Robert therefore decides that he will carry enough cash so that he will be able to meet demand (not run out of US dollars) on all but 2.5% of nights during the high season. How much should Robert carry in US dollars?

So I completely understand how to work out z-scores and working out the probability for example like - what is the probability on any given night that demand will exceed $16,000. however, I just cant seem to get my head around where to start with this problem. So some things i began to think about is which side of the bell curve is going to help me answer the question, and i think it will be on the left hand side.
I suppose the formula i need to use is:
x= mean + (z score x standard deviation)

but my confusion lies in whether Robert should be carrying more then the mean of $15,000 to meet all demand except for on 2.5% of nights or less than $15,000 to meet all demand except for on 2.5% nights. I am inclined to say less than $15,000- am I on the right track?
Really appreciate any help you can provide

 
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