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Normal Models and Standardized Scores

Algebra Foundation

Algebra 2

Explore advanced functions, complex numbers, polynomials, rational and radical expressions, exponentials, logarithms, conics, sequences, introductory trigonometry, probability, and statistics.

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Algebra 2 · Unit 12 · Topic 12.2

Normal Models and Standardized Scores

A normal model is a symmetric bell-shaped distribution specified by mean μ and positive standard deviation σ.

Definition and explanation

A normal model is a symmetric bell-shaped distribution specified by mean μ and positive standard deviation σ. The standardized score z = (x − μ)/σ expresses distance from the mean in standard-deviation units; not every dataset follows a normal model.

Worked example

Suppose a model has μ = 70 and σ = 8. A value of 86 has z = (86 − 70)/8 = 2, meaning it is two standard deviations above the mean. This calculation alone does not establish that the dataset is normal.

Common mistake

A z-score is not itself a probability or a percentile.

Key takeaway

A normal model is a symmetric bell-shaped distribution specified by mean μ and positive standard deviation σ.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.