Pierre operates a currency exchange office at Orly Airport in Paris. His office is open at night when the airport bank is closed, and he makes most of his business on returning U.S. tourists who need to change their remaining euros back to U.S. dollars. From experience, Pierre knows that the demand for dollars on any given night during high season is approximately normally distributed with mean $25,000 and standard deviation $5,000. If Pierre carries too much cash in dollars overnight, he pays a penalty: interest on the cash. On the other hand, if he runs short of cash during the night, he needs to send a person downtown to an all-night financial agency to get the required cash. This, too, is costly to him. Therefore, Pierre would like to carry overnight an amount of money such that the demand on 85% of the nights will not exceed this amount. Can you help Pierre find the required amount of dollars to carry?
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