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.

Z = 1.095.

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.

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.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer is 1

step-by-step explanation: