Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 9. Steve has a score of 52. Convert Steve's score to a z-score.
Question
Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 9. Steve has a score of 52. Convert Steve's score to a z-score.
Solution
The z-score is a measure of how many standard deviations an element is from the mean. To calculate the z-score, you subtract the mean from the element and then divide by the standard deviation.
Here's the step-by-step calculation for Steve's z-score:
- Subtract the mean: 52 (Steve's score) - 64 (mean) = -12
- Divide by the standard deviation: -12 / 9 (standard deviation) = -1.33
So, Steve's z-score is -1.33. This means Steve's score is 1.33 standard deviations below the mean.
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