The joint probability distribution of the weekly demand for two brands of diet soda is provided in the file S04_29.xlsx. In particular, let D1 and D2 represent the weekly demand (in hundreds of two-liter bottles) for brand 1 and brand 2, respectively, in a small town in central Indiana.
a. Find the mean and standard deviation of this community’s weekly demand for each brand of diet soda.
b. What is the probability that the weekly demand for each brand will be at least one standard deviation above its mean?
c. What is the probability that at least one of the two weekly demands will be at least one standard deviation above its mean?
d. What is the correlation between the weekly demands for these two brands of diet soda? What does this measure of association tell you about the relationship between these two products?