Question: The weekly demand function for one of a given firm's products can be represented by q = 200 - 5 p, where q is the number of units purchased (in hundreds) at price p (in dollars). Assume that the price of the product will be an integer value from $10 to $15, with probabilities 0.10, 0.15, 0.25, 0.30, 0.15, and 0.05.

a. Find the mean and standard deviation of p.

b. Find the mean and standard deviation of q.

c. Assuming that it costs this firm $10 to manufacture and sell each unit of the product, express the firm's weekly contribution to profit from the sale of this product (measured in dollars), as a function of the quantity purchased, q.

d. Find the mean and standard deviation of weekly contribution to the firm's profit from the sale of this product.