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levacccp [35]
2 years ago
9

Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points. Rachel scored 78 p

oints on an exam that had a mean score of 75 points and a standard deviation of 3.7 points. Find Keenan's and Rachel’s z-scores, to the nearest hundredth.
Mathematics
1 answer:
Artemon [7]2 years ago
6 0

Answer:

Keenan's z-score was of 0.61.

Rachel's z-score was of 0.81.

Step-by-step explanation:

Z-score:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points.

This means that X = 80, \mu = 77, \sigma = 4.9

So

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

Z = \frac{80 - 77}{4.9}

Z = 0.61

Keenan's z-score was of 0.61.

Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3.7 points.

This means that X = 78, \mu = 75, \sigma = 3.7. So

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

Z = \frac{75 - 78}{3.7}

Z = 0.81

Rachel's z-score was of 0.81.

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