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 below 252.75 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 252.75

P(X < x) =

2.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

3.Medium

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 35.8 min. Round z to two decimals.

μ_X = 12, σ_X = 1.5μ_Y = 20, σ_Y = 2X + Y > 35.8 min

P =

4.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 250.25 and 260.25 g? Give P as a decimal.

μ = 250σ = 5x₁ = 250.25x₂ = 260.25

P =

5.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 65σ = 10P = 99%

x = points

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 5% of them lie (the 5th percentile).

μ = 65σ = 10P = 5%

x = points

Answer key

1. P(X < x) = 0.7088
2. σ = 0.5 mm
3. P = 0.06426
4. P = 0.4599
5. x = 88.26 points
6. x = 48.55 points

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