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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 microf
percentage of women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter? Round to two decimal places.
A.
O B.
O C.
D.

Ask by Lawson Bowers. in the United States
Mar 21,2025

Solución de inteligencia artificial de Upstudy

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The percentage of women with red blood cell counts between 4.2 and 5.4 million cells per microliter is approximately 82.26%.

Solución

Let the red blood cell counts be normally distributed with a mean
million cells per microliter and a standard deviation
To find the percentage of women with counts in the range from to million cells per microliter, we standardize using the -score formula:
Step 1: Compute the -score for the lower limit :
Step 2: Compute the -score for the upper limit :
Step 3: Find the probability :
Using the standard normal distribution table or a calculator,
So, the probability that a woman’s red blood cell count falls between and million is:
Expressed as a percentage (rounded to two decimal places), this is about .
Since the closest answer provided is:
A.
the answer is A.

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Mind Expander

To determine the percentage of women with red blood cell counts in the normal range of 4.2 to 5.4 million cells per microliter, we can use the Z-score formula to find the Z-scores for both the lower limit (4.2) and the upper limit (5.4).
Z = (X - μ) / σ
For the lower limit (4.2 million):
Z1 = (4.2 - 4.577) / 0.382 ≈ -0.99
For the upper limit (5.4 million):
Z2 = (5.4 - 4.577) / 0.382 ≈ 2.15
Using a standard normal distribution table or calculator, we find:
  • The area to the left of Z1 (-0.99) is approximately 0.1611.
  • The area to the left of Z2 (2.15) is approximately 0.9842.
To find the percentage of women in the normal range, we subtract the area corresponding to Z1 from the area corresponding to Z2:
0.9842 - 0.1611 = 0.8231, or 82.31% when rounded to two decimal places.
Thus, the correct answer is A. .

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