The annual per capita consumption of fresh apples (in pounds) in a nearby state

Question

The annual per capita consumption of fresh apples (in pounds) in a nearby state can be approximated by a normal distribution, with a mean of 17.4 pounds and a standard deviation of 4.2 pounds. (a) What is the smallest annual per capita consumption of apples that can be in the top 25% of consumptions? (b) What is the largest annual per capita consumption of apples that can be in the bottom 15% of consumptions? of the table. Click to view page 2 of the table. (a) Any per capita consumption of at least (Round to two decimal places as needed.) pounds is in the top 25% of consumptions.

Explanation / Answer

Ans:

Given that

mean=17.4

standard deviation=4.2

a)Top 25% means that

P(Z>=z)=0.25

P(Z<=z)=1-0.25=0.75

z=0.6745

x=17.4+0.6745*4.2=20.23

b)Bottom 15% means that

P(Z<=z)=0.15

z=-1.036

x=17.4-1.036*4.2=13.05

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