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Flura [38]
3 years ago
8

A basketball coach kept stats for his team in free throw percentage and steals (among others). At the last game, Erin's free thr

ow percentage was 79% and she had 4 steals. The team averaged 87% from the free throw line with a standard deviation of 12 and they averaged 7 steals with a standard deviation of 3. In which category did Erin do better compared with her team
Mathematics
1 answer:
Setler79 [48]3 years ago
6 0

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 \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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

The team averaged 87% from the free throw line with a standard deviation of 12, which means that \mu = 87, \sigma = 12. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{79 - 87}{12}

Z = -0.67

Steals:

She had 4 steals, which means that X = 4

Averaged 7 steals with a standard deviation of 3, which means that \mu = 7, \sigma = 3. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{4 - 7}{3}

Z = -1

Due to the higher z-score, she did better in the free throw category.

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