Practice Z-Score in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A z-score measures how many standard deviations a data value is above or below the mean: z=(x−μ)/σ.

A universal measuring stick—z=2 means '2 SDs above average.'

Showing a random 20 of 50 problems.

Example 1

medium
A value has z-score 1.2. After every data value (including this one) is doubled, what is its new z-score?

Example 2

easy
A data point has value 45 in a distribution with μ=50 and σ=4. Find its z-score.

Example 3

medium
A normal distribution has μ=100. A value of 115 has z-score 1.5. Find σ.

Example 4

easy
A z-score is 2 with μ=50, σ=10. What is the raw value x?

Example 5

medium
On a normal distribution with μ=0, σ=1, what is the z-score of x=1.96?

Example 6

easy
A student scored 82 on an exam where the mean was 74 and the standard deviation was 8. What is the student's z-score?

Example 7

medium
Find the z-score for x=2, μ=8, σ=3.

Example 8

medium
A test has μ=60, σ=12. What raw score corresponds to the 84th percentile (normal data)?

Example 9

medium
A value with z-score 1.2 has every value in the dataset shifted up by 7. What is the value's new z-score?

Example 10

easy
Find the z-score for x=85, μ=70, σ=15.

Example 11

easy
A value equals the mean. What is its z-score?

Example 12

medium
A normal distribution has μ=200 and σ=25. What raw value has z-score −1.6?

Example 13

medium
A z-score of 2.5 corresponds to x=95. If σ=6, find μ.

Example 14

medium
Two raw scores have z-scores −0.5 and +2. Their difference is 20. Find σ.

Example 15

medium
Heights are normal with μ=170 cm and σ=8 cm. A person is 182 cm tall. What is the z-score?

Example 16

medium
On a normal distribution, a z-score of +2 means the value is in roughly what top percent?

Example 17

easy
Find the z-score for x=4, μ=10, σ=2.

Example 18

easy
A car gets 32 mpg. The fleet has μ=28 mpg and σ=4 mpg. Compute the z-score and describe what it means.

Example 19

hard
In a normal distribution, approximately what percent of values have ∣z∣≤2?

Example 20

medium
On Test A, Maria scored 78 (μ=70, σ=5). On Test B, she scored 85 (μ=80, σ=10). On which test did she perform relatively better?
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