Let’s solve each part step by step.
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Problem 1: Z-Score Worksheet
We are told the standard deviation (σ) is
10 for all parts of Question 1.
The formula for a z-score is:
>
z = (X - μ) / σ
Where:
- X = the score value
- μ = mean
- σ = standard deviation
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a) A score of 60, where the mean is 40.
Plug into the formula:
z = (60 - 40) / 10 = 20 / 10 =
2
✔ So, z = 2
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b) A score that is 30 points below the mean.
That means: X = μ - 30
So, z = (μ - 30 - μ) / 10 = (-30) / 10 =
-3
✔ So, z = -3
*(Note: The actual mean doesn’t matter here — we’re just looking at how far below it the score is.)*
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c) A score of 80, where the mean is 30.
z = (80 - 30) / 10 = 50 / 10 =
5
✔ So, z = 5
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d) A score of 20, where the mean is 50.
z = (20 - 50) / 10 = (-30) / 10 =
-3
✔ So, z = -3
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Now,
Question 2: IQ Scores
Given:
- Mean (μ) = 100
- Standard deviation (σ) = 16
- Einstein’s IQ (X) = 160
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a. What is the difference between Einstein’s IQ and the mean?
Difference = 160 - 100 =
60
✔ Answer: 60
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b. How many standard deviations is that?
We divide the difference by the standard deviation:
60 ÷ 16 = 3.75
✔ Answer: 3.75 standard deviations
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c. Convert Einstein’s IQ score to a z score.
Use the z-score formula:
z = (160 - 100) / 16 = 60 / 16 =
3.75
✔ Answer: 3.75
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Final Answer:
1a) 2
1b) -3
1c) 5
1d) -3
2a) 60
2b) 3.75
2c) 3.75
Parent Tip: Review the logic above to help your child master the concept of z score worksheet.
