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 and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.

μ_X = 250 g, σ_X = 4 gμ_Y = 500 g, σ_Y = 9 g

σ = g

2.Easy

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

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

σ = mm

3.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 50 and 73 points? Give P as a decimal.

μ = 65σ = 10x₁ = 50x₂ = 73

P =

4.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 24.8 and 44.3 min? Give P as a decimal.

μ = 32σ = 6x₁ = 24.8x₂ = 44.3

P =

5.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 75% of them lie (the 75th percentile).

μ = 250σ = 5P = 75%

x = g

6.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded bottom 5% is to the left of it. Find the cut-off x.

μ = 250 gσ = 5 g5%

x = g

Answer key

1. σ = 9.849 g
2. σ = 0.5 mm
3. P = 0.7213
4. P = 0.8647
5. x = 253.4 g
6. x = 241.8 g

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