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Z-Scores on a Normal Distribution: Public Worked Question

A public statistics question that shows how to standardize a raw score into a z-score using the mean and standard deviation.

Question

Scores on a placement exam are normally distributed with mean 150150 and standard deviation 88. A student scores 162162. What is the student's z-score?

  1. a.−1.5-1.5
  2. b.0.670.67
  3. c.1.51.5
  4. d.1212

Correct answer

C. 1.51.5

Full reasoning

  1. 1Find the deviation of the score from the mean: 162−150=12162 - 150 = 12.
  2. 2Divide the deviation by the standard deviation: z=12÷8=1.5z = 12 \div 8 = 1.5.
  3. 3The positive sign confirms the score lies 1.51.5 standard deviations above the mean of 150150.

Why each choice is right or wrong

Choice A

This reverses the subtraction, computing (150−162)/8(150 - 162)/8, which would describe a score below the mean rather than above it.

Choice B

This inverts the final division, computing 8/128/12 instead of dividing the deviation 1212 by the standard deviation 88.

Choice C

Correct. The deviation from the mean is 162−150=12162 - 150 = 12, and 12÷8=1.512 \div 8 = 1.5 standard deviations above the mean.

Choice D

This stops at the raw deviation 162−150162 - 150 and never divides by the standard deviation, so it is not a standardized score.

Related formula

Z-score of a value

z=x−μσz = \frac{x - \mu}{\sigma}

Assumptions: The standard deviation is positive so the division is defined.

Related topic and practice

Descriptive StatisticsSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. Introductory Statistics 2e, Section 6.1: The Standard Normal Distribution — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

Source-checked by publisher
Publisher record
Keiko Study editorial owner
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Reviewer record
Technical reviewer pending
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Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major preparation cycle.

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