Question

Question:The annual per capita consumption of fresh bananas? can be approximated by the normal? distribution, with a mean of 10.6 pounds and a standard deviation of 3 pounds.

?   a) What is the smallest annual per capita consumption of bananas that can be in the top 5?% of? consumptions?

?   b) What is the largest annual per capita consumption of bananas that can be in the bottom 10?% of? consumptions?

Answer 1

Solution :

mean = = 10.6

standard deviation = = 3

Using standard normal table,

a ) P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05 = 0.95

P(Z < 1.645 ) = 0.95

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 3 + 10.6

= 15.535

The smallest annual per capita consumption of bananas = 15.5

b ) Using standard normal table,

P(Z < z) = 10%

P(Z < z) = 0.10

P(Z < -1.282 ) = 0.10

z = -1.282

Using z-score formula,

x = z * +

x = - 1.282 * 3 + 10.6

= 6.754

The larest annual per capita consumption of bananas = 6.8