Practice Z-Score in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

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

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

Showing a random 20 of 50 problems.

Example 1

medium
A value has z-score 1.21.2. After every data value (including this one) is doubled, what is its new z-score?

Example 2

easy
A data point has value 4545 in a distribution with μ=50\mu = 50 and σ=4\sigma = 4. Find its z-score.

Example 3

medium
A normal distribution has μ=100\mu=100. A value of 115115 has z-score 1.51.5. Find σ\sigma.

Example 4

easy
A z-score is 22 with μ=50\mu=50, σ=10\sigma=10. What is the raw value xx?

Example 5

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

Example 6

easy
A student scored 8282 on an exam where the mean was 7474 and the standard deviation was 88. What is the student's z-score?

Example 7

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

Example 8

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

Example 9

medium
A value with z-score 1.21.2 has every value in the dataset shifted up by 77. What is the value's new z-score?

Example 10

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

Example 11

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

Example 12

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

Example 13

medium
A z-score of 2.52.5 corresponds to x=95x = 95. If σ=6\sigma = 6, find μ\mu.

Example 14

medium
Two raw scores have z-scores −0.5-0.5 and +2+2. Their difference is 2020. Find σ\sigma.

Example 15

medium
Heights are normal with μ=170\mu = 170 cm and σ=8\sigma = 8 cm. A person is 182182 cm tall. What is the z-score?

Example 16

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

Example 17

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

Example 18

easy
A car gets 3232 mpg. The fleet has μ=28\mu = 28 mpg and σ=4\sigma = 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|z| \leq 2?

Example 20

medium
On Test A, Maria scored 7878 (μ=70\mu = 70, σ=5\sigma = 5). On Test B, she scored 8585 (μ=80\mu = 80, σ=10\sigma = 10). On which test did she perform relatively better?
← Back to Z-Score Worked Examples Formula Explained