To calculate Isaac's z-score, you can use the formula for the z-score:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \(X\) is the value (number of candies received),
- \(\mu\) is the mean (average number of candies),
- \(\sigma\) is the standard deviation.
Given:
- \(X = 40\)
- \(\mu = 50\)
- \(\sigma = 12\)
Substituting these values into the formula, we have:
\[ z = \frac{(40 - 50)}{12} = \frac{-10}{12} \approx -0.8333 \]
Rounding to the nearest hundredth, Isaac's z-score is:
\[ z \approx -0.83 \]
For Trina, who received 47 pieces of candy, we can calculate her z-score in the same way:
\[ z = \frac{(X - \mu)}{\sigma} \]
Using:
- \(X = 47\)
- \(\mu = 50\)
- \(\sigma = 12\)
Substituting these values:
\[ z = \frac{(47 - 50)}{12} = \frac{-3}{12} = -0.25 \]
Trina's z-score is negative (-0.25).
The z-score is negative because Trina received fewer candies than the average (50). In general, when a value is below the mean, the z-score will be negative; when it is above the mean, the z-score will be positive. Therefore, Trina's z-score will be negative.