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 8.3 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?

(a) The smallest annual per captita consumption of bananas that can be in the top 10​% of consumptions is
__ pounds.

b) The largest annual per capita consumption of bananas that can be in the bottom 5​% of consumptions is
__pounds.

Answer 1

Given that,

mean = = 8.3

standard deviation = = 2

(a)

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 2 + 8.3 = 11.59

The smallest annual per capita consumption of bananas that can be in the top 10​% of consumptions is 10.86 pounds.

(b)

P(Z < -1.645) = 0.05

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 2 + 8.3 = 5.01

The largest annual per capita consumption of bananas that can be in the bottom 5​% of consumptions is 5.01 pounds.