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Costco plans on stocking a Christmas tree for the holiday season. The product is only sold in November and December. The order lead time is longer than two months so Costco can only place one order for the Christmas tree. Based on historical sales, Costco believes that the demand for the tree during the season is normally distributed with an average of 450 units and a standard deviation of 180 units. Costco purchases the trees at $79 each and sells them at $180 each. Any unsold tree at the end of the year will be sold to a discounted store at $55 each. Costco currently purchase 525 trees.
a. What is the probability that Costco will run out of stock before end of December?
b. What is the expected number of unsold trees at the end of December?
c. What is Costco’s expected profit from selling the tree?
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