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%.

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.

Step-by-step explanation:

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

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

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:

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.

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.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.