A pizza shop sells pizzas in 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 0.11 0.29 0.49 0.06
(a) Write a few sentences describing what you would expect to see for pizza sizes over a long sequence
of single-pizza orders. (Give your answers as percents.)
Fill in the blanks
In the long run, we would expect to see approximately _____ % of the single-pizza orders for 12 inch pizza, ______ % for 14 inch pizza, ______ % for 16 inch pizza, and _________ % for 18 inch pizza.
(b) What is the approximate value of P(x < 16)?
(c) What is the approximate value of P(x ≤ 16)?
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(a) In the long run, we would expect to see approximately 11% of the single-pizza orders for a 12-inch pizza, 29% for a 14-inch pizza, 49% for a 16-inch pizza, and 6% for an 18-inch pizza.
(b) P(x < 16) refers to the probability of selecting an order for a pizza size less than 16 inches. Since the proportion for the 12-inch pizza is 0.11 and the proportion for the 14-inch pizza is 0.29, we can estimate P(x < 16) as 0.11 + 0.29 = 0.4 or 40%.
(c) P(x ≤ 16) refers to the probability of selecting an order for a pizza size less than or equal to 16 inches. Since the proportion for the 12-inch pizza is 0.11, the proportion for the 14-inch pizza is 0.29, and the proportion for the 16-inch pizza is 0.49, we can estimate P(x ≤ 16) as 0.11 + 0.29 + 0.49 = 0.89 or 89%.
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