Quantity to Achieve In-stock Probability: 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 250 gallons and a standard deviation of 80 gallons. Goop sells the polymer for $25 per gallon. Goops purchases raw material for $10 per gallon and Goop must spend $5 per gallon to dispose of all unused raw material due to government regulations. (Assume one gallon of raw material yields one gallon of polymer with no extra cost.) If demand is more than Goop can make, then Goop sells only what they made and the rest of the demand is lost. Suppose Goop wants to ensure that there is a 80% probability that they will be able to satisfy the customers entire demand. How many gallons of the raw material should they purchase? Please show your work.

Less than 150

At least 150, but less than 200

At least 200, but less than 250

At least 250, but less than 300

At least 300, but less than 350

At least 350, but less than 400

At least 400, but less than 450

At least 450