To determine whether Trina's z-score will be positive or negative, we need to understand the concept of a z-score. A z-score indicates how many standard deviations a data point is from the mean of a distribution.
The formula for calculating a z-score is:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( X \) is the data point (in this case, the number of pieces of candy Trina received, which is 47),
- \( \mu \) is the mean of the distribution (the average number of candies received by all trick-or-treaters in that neighborhood),
- \( \sigma \) is the standard deviation of the distribution.
To determine whether Trina's z-score will be positive or negative, we need to compare the number of candies she received (47) to the mean (\( \mu \)).
- If 47 is greater than the mean (\( \mu \)), then Trina's z-score will be positive.
- If 47 is less than the mean (\( \mu \)), then Trina's z-score will be negative.
Without knowing the mean and standard deviation of the number of candies received by trick-or-treaters in that neighborhood, we cannot definitively determine the sign of the z-score. However, if you provide the mean or indicate whether the number of candies she received is above or below average for that neighborhood, I could help you conclude whether the z-score is positive or negative.