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. Fin
for the red blood cell counts of women. Round to three decimal places.
A. 4.898 million cells per microliter
B. 4.655 million cells per microliter
C. 4.878 million cells per microliter

Question

UpStudy AI · Accepted Answer

To find the red blood cell counts of women, we need to determine the values that correspond to certain percentiles in a normal distribution. Given the mean ($$ \mu $$) and standard deviation ($$ \sigma $$):

- Mean ($$ \mu $$) = 4.577 million cells per microliter
- Standard Deviation ($$ \sigma $$) = 0.382 million cells per microliter

We will calculate the values for the specified options and see which one corresponds to the normal distribution.

1. **Calculate the z-scores for each option**:
   - For option A: $$ 4.898 $$
   - For option B: $$ 4.655 $$
   - For option C: $$ 4.878 $$

The z-score formula is given by:

$$
z = \frac{X - \mu}{\sigma}
$$

where $$ X $$ is the value we are evaluating.

Let's calculate the z-scores for each option.

### Step 1: Calculate z-scores

1. For option A: $$ X = 4.898 $$
2. For option B: $$ X = 4.655 $$
3. For option C: $$ X = 4.878 $$

Now, I will calculate the z-scores for these values.

### Step 2: Calculate z-scores

- For option A:
$$
z_A = \frac{4.898 - 4.577}{0.382}
$$

- For option B:
$$
z_B = \frac{4.655 - 4.577}{0.382}
$$

- For option C:
$$
z_C = \frac{4.878 - 4.577}{0.382}
$$

Now, I will perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(4.878-4.577\right)}{0.382}$$
- step1: Remove the parentheses:
  $$\frac{4.878-4.577}{0.382}$$
- step2: Subtract the numbers:
  $$\frac{0.301}{0.382}$$
- step3: Convert the expressions:
  $$\frac{\frac{301}{1000}}{\frac{191}{500}}$$
- step4: Multiply by the reciprocal:
  $$\frac{301}{1000}\times \frac{500}{191}$$
- step5: Reduce the numbers:
  $$\frac{301}{2}\times \frac{1}{191}$$
- step6: Multiply the fractions:
  $$\frac{301}{2\times 191}$$
- step7: Multiply:
  $$\frac{301}{382}$$
Calculate or simplify the expression $$ (4.898 - 4.577) / 0.382 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(4.898-4.577\right)}{0.382}$$
- step1: Remove the parentheses:
  $$\frac{4.898-4.577}{0.382}$$
- step2: Subtract the numbers:
  $$\frac{0.321}{0.382}$$
- step3: Convert the expressions:
  $$\frac{\frac{321}{1000}}{\frac{191}{500}}$$
- step4: Multiply by the reciprocal:
  $$\frac{321}{1000}\times \frac{500}{191}$$
- step5: Reduce the numbers:
  $$\frac{321}{2}\times \frac{1}{191}$$
- step6: Multiply the fractions:
  $$\frac{321}{2\times 191}$$
- step7: Multiply:
  $$\frac{321}{382}$$
Calculate or simplify the expression $$ (4.655 - 4.577) / 0.382 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(4.655-4.577\right)}{0.382}$$
- step1: Remove the parentheses:
  $$\frac{4.655-4.577}{0.382}$$
- step2: Subtract the numbers:
  $$\frac{0.078}{0.382}$$
- step3: Convert the expressions:
  $$\frac{\frac{39}{500}}{\frac{191}{500}}$$
- step4: Multiply by the reciprocal:
  $$\frac{39}{500}\times \frac{500}{191}$$
- step5: Reduce the numbers:
  $$39\times \frac{1}{191}$$
- step6: Multiply:
  $$\frac{39}{191}$$
The calculated z-scores for each option are as follows:

1. For option A ($$4.898$$):
   $$
z_A \approx 0.840
   $$

2. For option B ($$4.655$$):
   $$
z_B \approx 0.204
   $$

3. For option C ($$4.878$$):
   $$
z_C \approx 0.788
   $$

### Conclusion
Now, we can compare these z-scores to determine which option corresponds to the red blood cell counts of women.

- Option A: $$4.898$$ has a z-score of approximately $$0.840$$.
- Option B: $$4.655$$ has a z-score of approximately $$0.204$$.
- Option C: $$4.878$$ has a z-score of approximately $$0.788$$.

Since the question asks for the red blood cell counts of women, we can conclude that the option with the highest z-score (which is closest to the mean) is likely the most representative of the normal distribution.

Thus, the answer is **Option A: 4.898 million cells per microliter**.
The red blood cell count is 4.898 million cells per microliter.

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Step 1: Calculate z-scores

Step 2: Calculate z-scores

Conclusion

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