The amount of cholesterol in a person's body produced by the liver and other cells is proposed to be Normally distributed with mean 75% and standard deviation 0.5%.
What is the first quartile of the distribution of cholesterol production?

Question

Quizplus · Accepted Answer

To find the first quartile, we need to find the value that separates the lowest 25% of the distribution from the rest. We can use the z-score formula to find the corresponding value:

z = (Q1 - μ) / σ

where Q1 is the first quartile, μ is the mean, σ is the standard deviation, and z is the z-score that corresponds to the 25th percentile, which is -0.6745 (from standard normal distribution tables).

Substituting the given values, we get:

-0.6745 = (Q1 - 0.75) / 0.005

Solving for Q1, we get:

Q1 = 0.75 + (-0.6745) x 0.005 = 0.7466 or 74.66%

Therefore, the first quartile of the distribution of cholesterol production is 74.66%. Option A is correct.

The Amount of Cholesterol in a Person's Body Produced by the Liver