Math

QuestionFind the ZZ-score for a student who scored 74 on a test with an average of 80 and a standard deviation of 6.

Studdy Solution

STEP 1

Assumptions1. The average (mean) score on the Literature test is80. . The standard deviation of the scores is6.
3. The score of the student in question is74.
4. We are asked to find the ZZ-score, which is a measure of how many standard deviations an element is from the mean.

STEP 2

The formula for calculating the ZZ-score is as followsZ=(Xμ)σZ = \frac{(X - \mu)}{\sigma}WhereZZ is the ZZ-score, XX is the score of the student, μ\mu is the mean score, andσ\sigma is the standard deviation.

STEP 3

Now, plug in the given values for the student's score, the mean score, and the standard deviation into the ZZ-score formula.
Z=(7480)6Z = \frac{(74 -80)}{6}

STEP 4

Calculate the difference between the student's score and the mean score.
7480=674 -80 = -6So, we haveZ=66Z = \frac{-6}{6}

STEP 5

Finally, calculate the ZZ-score by dividing the difference by the standard deviation.
Z==1Z = \frac{-}{} = -1The ZZ-score of the student who earned a74 on the test is -1.

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