Safeway stocks national brands of coffee, as well as its own house brand. Consider a single randomly selected customer purchasing coffee and let "success" = the customer purchases a national brand. Assume p = 0.75, and that customers make coffee purchase decisions independently of one another. Also, assume that X = number among 20 randomly selected coffee purchasers who select a national brand, and that the random variable X follows the binomial distribution.

a. What is the probably that at most 15 customers choose a national brand?

b. What is the probability that exactly 15 customers choose a national brand?

c. What is the probability that at least 12 customers select a national brand?

d. Calculate the mean (i.e., the expected value) and the variance of the random variable X.