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Sagot :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]X = 79[/tex]
The team averaged 87% from the free throw line with a standard deviation of 12, which means that [tex]\mu = 87, \sigma = 12[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{79 - 87}{12}[/tex]
[tex]Z = -0.67[/tex]
Steals:
She had 4 steals, which means that [tex]X = 4[/tex]
Averaged 7 steals with a standard deviation of 3, which means that [tex]\mu = 7, \sigma = 3[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4 - 7}{3}[/tex]
[tex]Z = -1[/tex]
Due to the higher z-score, she did better in the free throw category.
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