U. S. women aged 20 or over have a mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl. Assume that the distribution is Normal. What proportion of women have HDL below 45 mg/dl or less?

0.2514 = 25.14% of women have HDL below 45 mg/dl or less.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl.

This means that

What proportion of women have HDL below 45 mg/dl or less?

This is the p-value of Z when X = 45. So

has a p-value of 0.2514

0.2514 = 25.14% of women have HDL below 45 mg/dl or less.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,