Question

The cholesterol levels for U.S. adults are normally distributed with a mean of 222 and a standard deviation of 46. What cholesterol level separates the lowest 16%?

If there are two answers, list both answers separated by a comma.

Answer 1

To find the cholesterol level that separates the lowest 16% of U.S. adults, we use the z-score for the 16th percentile (approximately -1) and the given mean (222) and standard deviation (46). The cholesterol level is calculated to be 176.

Step-by-step explanation:

The question asks to find the cholesterol level that separates the lowest 16% of U.S. adults given that the levels are normally distributed with a mean of 222 and a standard deviation of 46. To solve this, we'll need to find the z-score that corresponds to the lowest 16% of the distribution, and then use the mean and standard deviation to find the cholesterol level.

We know that the z-score for the 16th percentile is approximately -1 since 16% is close to one standard deviation below the mean on a normal distribution. Using the z-score formula:

Z = (X - Mean) / Standard Deviation

We can re-arrange to solve for X, which represents the cholesterol level:

X = Z * Standard Deviation + Mean

Plugging in the values, we get:

X = -1 * 46 + 222 = 176

Therefore, the cholesterol level that separates the lowest 16% is 176.