A supply company currently has in stock 500 lb of fertilizer, which it sells to customers in 10-pound bags. Let X equal the number of bags purchased by a randomly selected customer. Sales data shows that X has the following pmf:

a. Compute the average number of bags bought per customer.
b. Determine the standard deviation for the number of bags bought per customer.
c. Define Y to be the amount of fertilizer left in stock, in pounds, after the first customer. Construct the pmf of Y.
d. Use the pmf of Y to find the expected amount of fertilizer left in stock, in pounds, after the first customer.
e. Write Y as a linear function of X. Then use rescaling properties to find the mean and standard deviation of Y.
f. The supply company offers a discount to each customer based on the formula W = (X – 1)². Determine the expected discount for a customer.
g. Does your answer to part (f) equal (μ_X  – 1)²? Why or why not?
h. Calculate the standard deviation of W.

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