The average number of red blood cells in an adult male is 6.2 million cells per microliter, with a standard deviation of 0.6 million cells per microliter. If Sergio's blood contains 6.7 million cells per microliter, which option correctly calculates and interprets his z-score? (1 point)

Question

O Sergio's red blood cell count is 0.5 standard deviations above the mean.

O Sergio's red blood cell count is 0.833 standard deviations above the mean.

Sergio's red blood cell count is 0.5 standard deviations below the mean.

Sergio's red blood cell count is 0.833 standard deviations below the mean.

Answer 1

To calculate Sergio's z-score, we use the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where:

• \(X\) is Sergio's blood cell count,
• \(\mu\) is the mean blood cell count,
• \(\sigma\) is the standard deviation.

Given:

• \(X = 6.7\) million cells per microliter,
• \(\mu = 6.2\) million cells per microliter,
• \(\sigma = 0.6\) million cells per microliter.

Substituting these values into the formula:

\[ z = \frac{(6.7 - 6.2)}{0.6} = \frac{0.5}{0.6} \approx 0.8333 \]

This means that Sergio's red blood cell count is approximately 0.833 standard deviations above the mean.

Therefore, the correct interpretation is:

O Sergio's red blood cell count is 0.833 standard deviations above the mean.