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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.6985. Find z to two decimals.

A = 0.6985

z =

3.Medium

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 probability P that X + Y is more than 199.6 mm. Round z to two decimals.

μ_X = 120, σ_X = 0.3μ_Y = 80, σ_Y = 0.4X + Y > 199.6 mm

P =

4.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 45.5 and 85 points? Give P as a decimal.

μ = 65σ = 10x₁ = 45.5x₂ = 85

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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 100σ = 15P = 97.5%

x = points

Answer key

1. σ = 0.5 mm
2. z = 0.52
3. P = 0.7881
4. P = 0.9517
5. P = 0.7389
6. x = 129.4 points

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