Consider the pizza crust diameters for 10-inch pizzas given Exercise 17.11 (pages 768-769).

We found that, by removing an assignable cause, we were able to bring the process into statistical control with x̅̅ = 10.2225 and  = .825.

a. Recalling that the subgroup size for the pizza crust x and R charts is 5, and assuming that the pizza crust diameters are approximately normally distributed, calculate the natural tolerance limits for the diameters.

b. Using the natural tolerance limits, estimate the largest diameter likely to be sold by the restaurant as a 10-inch pizza.

c. Using the natural tolerance limits, estimate the smallest diameter likely to be sold by the restaurant as a 10-inch pizza.

d. Are all 10-inch pizzas sold by this restaurant really at least 10 inches in diameter? If not, estimate the fraction of pizzas that are not at least 10 inches in diameter.