Question

The population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.

i) Find the third quartile for the average cholesterol content for 25 eggs.

ii)If we are told the average for 25 eggs is less than 220 mg, what is the probability that the average is less than 210.

Answer 1

i) = 215 mg

= 15 mg

P(X < A) = P(Z < (A - )/)

Let the third quartile be Q3

P(X < Q3) = 0.75

P(Z < (Q3 - 215)/15) = 0.75

Take value of Z corresponding to 0.75 from standard normal distribution table

(Q3 - 215)/15) = 0.67

Q3 = 225.05 mg

ii) Bayes' Theorem: P(A | B) = P(A & B)/P(B)

For sample of size n,

P( < A) = P(Z < (A - )/)

n = 25

= = 215 mg

=

=

= 3

P(average is less than 210 mg | average is less than 220 mg) = P( < 210) / P( < 220)

= P(Z < (210 - 215)/3) / P(Z < (220 - 215)/3)

= P(Z < -1.67) / P(Z < 1.67)

= 0.0475 / 0.9525

= 0.0499