Cholesterol levels for a group of women aged 40-49 follow an approximately normal distribution with mean 201.73 milligrams per deciliter (mg/dl). Medical guidelines state that women with cholesterol levels above 240 mg/dl are considered to have high cholesterol and about 13.7% of women fall into this category.
What is the Z-score that corresponds to the top 13.7% (or the 86.3-th percentile) of the standard normal distribution? Round your answer to three decimal places.

Question

02-03-2020
Mathematics

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Cholesterol levels for a group of women aged 40-49 follow an approximately normal distribution with mean 201.73 milligrams per deciliter (mg/dl). Medical guidelines state that women with cholesterol levels above 240 mg/dl are considered to have high cholesterol and about 13.7% of women fall into this category.
What is the Z-score that corresponds to the top 13.7% (or the 86.3-th percentile) of the standard normal distribution? Round your answer to three decimal places.

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joaobezerra joaobezerra · Answer 1 · 2020-03-02T20:00:57+01:00

Answer:

Z = 1.095.

Step-by-step explanation:

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

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

What is the Z-score that corresponds to the top 13.7% (or the 86.3-th percentile) of the standard normal distribution?

Looking at the z-table, it is Z when it has a pvalue of 0.863, which is between 1.09 and 1.10, so it is Z = 1.095.