The annual per capita consumption of ice cream (in pounds) in the United States

Question

The annual per capita consumption of ice cream (in pounds) in the United States can be approximated by the normal distribution, as shown in the figure to the right. (a) What is the largest annual per capita consumption of ice cream that can be in the bottom 14 14% of consumptions? (b) Between what two values does the middle 80% of the consumptions lie? 17 29 5 Consumption (in lbs) mu equals 16.6 =16.6 sigma equals 5.8 =5.8 x x y graph Click to view page 1 of the Standard Normal Table. LOADING... Click to view page 2 of the Standard Normal Table. LOADING... (a) The largest annual per captita consumption of ice cream that be in the bottom 14 14% of consumptions is nothing pounds. (Round to one decimal place as needed.) (b) The middle 80% of consumption lies between nothing and nothing pounds. (Round to one decimal place as needed.)

Explanation / Answer

a) z score corresponding to bottom 14% of area = -1.08

Hence,

Annual per capita consumption = 16.6 - 1.08*5.8 = 10.3 pounds

b) for middle 80% area, z scores = -1.28, 1.28

Hence,

Middle 80% area will lie between (16.6 - 1.28*5.8) and (16.6 + 1.28*5.8) i.e. 9.2 pounds and 24.0 pounds.

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