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MatroZZZ [7]
2 years ago
8

Mary and Jane both took PSY230 last semester but they were in two different sections taught by different professors. Mary's clas

s had a mean grade of 85 points with a standard deviation of 5 points while Jane's class had a mean grade of 80 points with a standard deviation of 10 points. Both Mary and Jane earned 88 points. Who did better in class
Mathematics
1 answer:
Greeley [361]2 years ago
4 0

Answer:

Due to the higher z-score, Jane did better in class.

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:

Whoever's grade had the better z-score did better in class.

Mary's:

Mean of 85, standard deviation of 5, grade of 88. This means that \mu = 85, \sigma = 5, X = 88. So

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

Z = \frac{88 - 85}{5}

Z = 0.6

Jane's

Mean of 80, standard deviation of 10, grade of 88. This means that \mu = 80, \sigma = 10, X = 88. So

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

Z = \frac{88 - 80}{10}

Z = 0.8

Due to the higher z-score, Jane did better in class.

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