Question

The annual per capita consumption of fresh bananas​ (in pounds) in the United States can be approximiated by the normal​ distribution, with a mean of 8.9 pounds and a standard deviation of 2 pounds. Answer the following questions about the specified normal distribution. ​(a) What is the smallest annual per capita consumption of bananas that can be in the top 10​% of​ consumptions? ​(b) What is the largest annual per capita consumption of bananas that can be in the bottom 5​% of​ consumption? Click to view page 1 of the Standard Normal Table. LOADING... Click to view page 2 of the Standard Normal Table. LOADING... ​(a) The smallest annual per captita consumption of bananas that can be in the top 10​% of consumptions is nothing pounds. ​(Round to one decimal place as​ needed.) ​(b) The largest annual per capita consumption of bananas that can be in the bottom 5​% of consumptions is nothing pounds. ​(Round to one decimal place as​ needed.)

Answer 1

Solution :

mean = = 8.9

standard deviation = = 2

Using standard normal table,

P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10 = 0.90

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 2 + 8.9 = 11.5

smallest annual per captita = 11.5 pounds

(b)

P(Z < z) = 5% = 0.05

P(Z < -1.645) = 0.05

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 2 + 8.9 = 5.6

largest annual per captita = 5.6 pounds