Question

In a randomly selected sample of 1169 men ages 35–44, the mean total cholesterol level was 210 milligrams per deciliter with a standard deviation of 38.6 milligrams per deciliter. Assume the total cholesterol levels are normally distributed. Find the highest total cholesterol level a man in this 35–44 age group can have and be in the lowest 10%.

Answer 1

The highest total cholesterol level a man in this 35–44 age group can have and be in the lowest 10% is 160.59 milligrams per deciliter.

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 210, \sigma = 38.6`

Find the highest total cholesterol level a man in this 35–44 age group can have and be in the lowest 10%.

This is the 10th percentile, which is X when Z has a pvalue of 0.1. So X when Z = -1.28.

`Z = (X - \mu)/(\sigma)`

`-1.28 = (X - 210)/(38.6)`

`X - 210 = -1.28*38.6`

`X = 160.59`

The highest total cholesterol level a man in this 35–44 age group can have and be in the lowest 10% is 160.59 milligrams per deciliter.