"Unbelievable!" Clark exclaimed as he slammed the remote control down on his coffee table. Clark, owner of the popular Clark's Pizza Emporium in downtown Metropolis, was enraged by a television advertisement for rival Lex's Pizza Shack. While Clark's business had been strong lately owing to the success of his signature product, the 18-inch "Superpizza," Lex was now threatening this success with a new offering, the "Megalopizza," which the ad claimed averaged a whopping 19 inches in diameter.

Clark has his doubts that Lex will be able to make good on his claims for two reasons. First, Lex has proven to be a less than honest competitor in the past. Second, Clark's study of pizza physics suggests that it is impossible to sustainably produce high-quality pizza at a size of 19 inches.

(4 pts) There is natural variability in the sizes of pies produced by any pizza operation. Suppose that diameters of Megalopizzas are normally distributed with a mean of 18.85 inches and a standard deviation of 0.35 inches. What is the probability that a single, randomly chosen pizza will have a diameter greater than 19.1 inches?

(4 pts) Suppose that the diameters of Megalopizzas are normally distributed with a mean of 18.85 inches and a standard deviation of 0.35 inches. If Clark samples 8 pizzas, what is the probability that the average size of the eight pizzas is greater than 19.1 inches?