a sample of 20 grades from a recent stats exam has a mean of 74.8 points (out of a possible 100 points) and a standard deviation of 15.5 points. calculate the z-score for the student who scored 79.6 points on the exam.

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15-12-2022
Mathematics

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a sample of 20 grades from a recent stats exam has a mean of 74.8 points (out of a possible 100 points) and a standard deviation of 15.5 points. calculate the z-score for the student who scored 79.6 points on the exam.

Answer :

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HafsaM HafsaM · Answer 1 · 2022-12-20T20:42:18-05:00

The test statistic for the student who scored 79.6 points on the exam is 1.38

The relationship between a value and the mean of a group of values is quantified by a Z-score. The Z-score is calculated using standard deviations from the mean. A Z-score of zero means the data point's score is equal to the mean score.

Formula for z-score = x - u / σ

According to the question,

Sample size = 20 grades

Mean of sample = 74.8

Sample Standard deviation = 15.5

We have to calculate z-score for the student who scored 79.6 points on the exam.

But here if we see , sample size is less than 30 and population standard deviation is unknown.

So, we can't use Z-score .

t-statistics = x - u / (s/√n)

=> 79.6 - 74.8 / ( 15.5 / √20)

=> 4.8√20 / 15.5

=> 1.38 is required answer

To know more about z-score here

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