Normal distribution worksheet with answers

Free printable Normal distribution worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is above 244.25 g? Find P(X > x) as a decimal.

μ = 250σ = 5x = 244.25

P(X > x) =

2.Easy

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 108.25 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 108.25

P(X < x) =

3.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 245 and 256.25 g? Give P as a decimal.

μ = 250σ = 5x₁ = 245x₂ = 256.25

P =

4.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 49 and 83 points? Give P as a decimal.

μ = 65σ = 10x₁ = 49x₂ = 83

P =

5.Hard

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 180 cm, σ_X = 10 cmμ_Y = 170 cm, σ_Y = 12 cm

P =

6.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 15% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h15%

x = h

Answer key

1. P(X > x) = 0.8749
2. P(X < x) = 0.7088
3. P = 0.7357
4. P = 0.9093
5. P = 0.7389
6. x = 542 h

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