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Answer:
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:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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](https://tex.z-dn.net/?f=%5Cmu%20%3D%20210%2C%20%5Csigma%20%3D%2038.6)
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 = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.28 = \frac{X - 210}{38.6}](https://tex.z-dn.net/?f=-1.28%20%3D%20%5Cfrac%7BX%20-%20210%7D%7B38.6%7D)
![X - 210 = -1.28*38.6](https://tex.z-dn.net/?f=X%20-%20210%20%3D%20-1.28%2A38.6)
![X = 160.59](https://tex.z-dn.net/?f=X%20%3D%20160.59)
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.
-2+6x+4+4x
=2+10x
hope it helps
The answer is the first one, (2)