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

10.1

pounds and a standard deviation of

3

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

given data are

population mean =10.1 pounds

population sd =3 pounds

in a z normal distribution

a) at top 10% i.e in right tail from z table at =10%

z=1.28

then x= 10.1+ 1.28 (3)

= 10.1+3.84= 13.94

b) ay bottom 5% i.e in left tail from z table at =5% z=-1.645

then x= 10.1- 1.645 (3)

=10.1- 4.935 = 5.165