. Rustic Dairy Products produces a line of artisanal organic ice cream. It sells its one flavor of ice cream to only two very exclusive organic restaurants, X and Y. Each Friday evening, the restaurants place orders with Rustic for the ice cream they will need in the following week. Of course, weekly demand for ice cream fluctuates randomly. Weekly demand from restaurant X is normally distributed with mean 200 gallons and standard deviation 30 gallons. Weekly demand from restaurant Y is normally distributed with a mean of 230 gallons and standard deviation 40 gallons. Orders are placed on Friday evening, the ice cream is made on Saturday, and delivered Sunday morning. The wholesale price of the ice cream (the price that Rustic receives) at both restaurants is $4 per gallon. (a) What is the probability that restaurant X will demand more than 220 gallons of ice cream in any given week? (b) What is the expected value and variance of the weekly total volume of ice cream demanded by the two restaurants? Assume that demands from the two restaurants are independent. (c) The key ingredient in Rustics ice cream is organic milk. It takes 12 pounds of milk to make a gallon of ice cream. Rustic has to plan its milk production well in advance of receiving orders. How much milk must Rustic have on hand at the end of each week to be able to meet demand for its ice cream in 90% of weeks? (d) Rustics management is suspicious of the assumption that demand at the two restaurants are independent. A careful examination of available financial records reveals that the standard deviation of revenue from its ice cream product is $252.9822. Calculate the correlation between restaurant demands implied by this figure.