Answer:
Due to the higher z-score, she did better in the free throw category.
Step-by-step explanation:
Z-score:
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
She did better in the category that she had the higher z-score:
Free-throws:
Her free throw percentage was 79%, which means that ![X = 79](https://tex.z-dn.net/?f=X%20%3D%2079)
The team averaged 87% from the free throw line with a standard deviation of 12, which means that
. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{79 - 87}{12}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B79%20-%2087%7D%7B12%7D)
![Z = -0.67](https://tex.z-dn.net/?f=Z%20%3D%20-0.67)
Steals:
She had 4 steals, which means that ![X = 4](https://tex.z-dn.net/?f=X%20%3D%204)
Averaged 7 steals with a standard deviation of 3, which means that
. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{4 - 7}{3}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B4%20-%207%7D%7B3%7D)
![Z = -1](https://tex.z-dn.net/?f=Z%20%3D%20-1)
Due to the higher z-score, she did better in the free throw category.