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 8.8 pounds and a standard deviation of 1 pound. 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?

Answer 1

Given that,

mean = = 8.8

standard deviation = = 1

(a)

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 1 + 8.8 = 10.08

smallest annual per capita = 10.08 pounds

(b)

P(Z < -1.645) = 0.05

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 1 + 8.8 = 7.155

Largest annual per Capita = 7.155 pounds