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

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of the difference X − Y.

μ_X = 120 mm, σ_X = 0.3 mmμ_Y = 80 mm, σ_Y = 0.4 mm

σ = mm

2.Easy

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 29 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 29

P(X < x) =

3.Medium

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 95.4 s. Round z to two decimals.

μ_X = 60, σ_X = 5μ_Y = 45, σ_Y = 4X + Y > 95.4 s

P =

4.Medium

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 167.85 and 192 cm? Give P as a decimal.

μ = 178σ = 7x₁ = 167.85x₂ = 192

P =

5.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 30% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points30%

x = points

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 20% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points20%

x = points

Answer key

1. σ = 0.5 mm
2. P(X < x) = 0.3085
3. P = 0.9332
4. P = 0.9037
5. x = 107.8 points
6. x = 56.6 points

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