UNIFORM EXAMPLE 3 I think a coffee dispenser machine fills cups at amounts that are uniformly distributed. Specifically, if I select a small 12 oz coffee, the machine dispenses between 10 and 13 oz. of coffee, following a uniform distribution. a) Is the amount of coffee dispensed by the machine a discrete or continuous random variable? Explain. b) Graph the probability function for P(X), where X is the amount of coffee dispensed when I select a small coffee. c) What is P( X = 12) ? d) Find the probability that my 12 oz. cup will not overflow, i.e. P( X 12). e) How large of a coffee cup should I have if I want to be 95% confident that the dispenser won't overfill the cup? (Hint: find P95)