The percent of fat calories that a person consumes each day is normally distribu

Question

The percent of fat calories that a person consumes each day is normally distributed with a mean of 34 and a standard deviation of 10. Suppose that 9 individuals are randomly chosen. Let

X = average percent of fat calories.

(a) For the group of 9, find the probability that the average percent of fat calories consumed is more than thirty-five. (Round your answer to four decimal places.)

b) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.)

I got part A correct (.3821) but I can't get part B.

Explanation / Answer

Ans:

Given that

mean=34

standard deviation=10

a)standard error of mean=10/sqrt(9)=10/3

z=(35-34)/(10/3)=3/10=0.3

P(z>0.3)=0.3821

b)First quartile means that

P(Z<=z)=0.25

z=-0.6745

average calorie=34-0.6745*(10/3)=31.75

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