Goop Inc. needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be normally distributed with a mean of 253 gallons and a standard deviation of 126 gallons. Goop sells the polymer for $25 per gallon. Goop purchases raw material for $10 per gallon and must spend $5 per gallon to dispose of all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what it has made and the rest of the demand is lost.

Suppose Goop wants to ensure that there is a 92% probability that they will be able to satisfy the customers entire demand. How many gallons of raw material should they purchase?

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