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

11.8

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?

Answer 1

We are given the distribution here as:

a) From standard normal tables, we have here:
P(Z < 1.282) = 0.9, that is: P(Z > 1.282) = 0.1

Therefore the smallest annual per capita consumption of bananas that can be in the top 10​% of​ consumptions is computed here as:
= 11.8 + 1.282*2 = 14.364
Therefore 14.364 pounds is the required value here.

b) From standard normal tables, we have here:
P(Z < -1.645) = 0.05

Therefore the largest per capita consumption here is computed as:
= Mean - 1.645*Sd

= 11.8 - 1.645*2

= 8.51

Therefore 8.51 pounds is the required value here.