The annual per capita consumption of ice cream in pounds in

The annual per capita consumption of ice cream (in pounds) in the us can be approximated by a normal distribution with a mean of 15.4 Ib and a sd of 2.5 Ib What is the smallest per capita ice cream consumption that can be in the top 25% of consumptions What is the largest annual per capita Ice cream consumption that can be in the bottom 15% of consumption

Solution

let x be the smallest per capita ice cream

6)

P( X >x) = 0.25

P(Z > x - 15.4/2.5) = 0.25

x-15.4/2.5 = 1 - invnorm(0.25)

x - 15.4/2.5 = 1 - (-0.674)

x = 19.585

7)

similalry

P(X < x) = 0.15

P(Z < x-15.4/2.5) = 0.15

x - 15.4/2.5 = invnorm(0.15)

x - 15.4/2.5 = -1.036

x = 12.81