Question

A pizza shop sells pizzas four different sizes. The 1,000 most recent orders for a single pizza resulted in the following proportions for the various sizes. Size (inches) 12 14 16 18 Proportion 0.15 0.30 0.50 0.05 With x the size of a pizza in a single-pizza order, the given table is an approximation to the population distribution of x. Write a few sentences describing what you would expect to see for pizza sizes over a long sequence of single-pizza orders. % for 14 inch pizza, % for 16 inch pizza, In the long run, we would expect to see approximately % of the single-pizza orders for 12 inch pizza, % for 18 inch pizza. and (b) What is the approximate value of P(x 16)? What is the approximate value of P(x s 16)?

Answer 1

(a) In the long run we would expect to see approximately 15 % of the single pizza orders for 12 inch pizza, 30% for 14 inch pizza, 60% for 16 inch pizza and 5% for 18 inch pizza.

(b) P(x<16) = P(x=12) + P(x=14) = 0.15 + 0.30 = 0.45

(c) P(x <= 16) = P(x=12) + P(x=14) + P(x=16)  = 0.15 + 0.30 0.50 = 0.95