Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per microliter. Approximately what percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter?

82.31% of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter

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:

Approximately what percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter?

This is the pvalue of Z when X = 5.4 subtracted by the pvalue of Z when X = 4.2. So

X = 5.4

has a pvalue of 0.9842

X = 4.2

has a pvalue of 0.1611

0.9842 - 0.1611 = 0.8231

82.31%  of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter

a

step-by-step explanation:

the answer is a