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)

Answer 1

To calculate the z-score for Sergio's red blood cell count, you can use the following formula:

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

Where:

• \(X\) is Sergio's blood cell count (6.7 million cells per microliter),
• \(\mu\) is the average number of red blood cells for adult males (6.2 million cells per microliter),
• \(\sigma\) is the standard deviation (0.6 million cells per microliter).

Plugging in the values:

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

\[ z = \frac{0.5}{0.6} \approx 0.8333 \]

Therefore, Sergio's z-score is approximately 0.83.

Interpretation:

A z-score of 0.83 indicates that Sergio's red blood cell count is 0.83 standard deviations above the mean for adult males. This means his count is higher than most adult males, as a positive z-score indicates a value above the average.