Home › US High School › Mathematics › The Standard Normal Distribution › A reading test is normal with mean 70 and standa…
A reading test is normal with mean 70 and standard deviation 8. Which z-score belongs to a mark of 86?
AThe z-score is 2
BThe z-score is 8
CThe z-score is 16
DThe z-score is 4
Answer & Solution
Correct answer: A. The z-score is 2
1. The mark sits above the mean, so the z-score will be positive.
2. Subtract the mean from the mark: 86 minus 70 is 16.
3. Divide that gap by the standard deviation of 8.
4. That gives a z-score of 2.
5. Answering 16 stops at the raw gap and never converts it into standard deviations.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 6 "The Normal Distribution", section 6.1 The Standard Normal Distribution_