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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9599. Find z to two decimals.

A = 0.9599

z =

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

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the probability P that X + Y is more than 735.2 g. Round z to two decimals.

μ_X = 250, σ_X = 4μ_Y = 500, σ_Y = 9X + Y > 735.2 g

P =

4.Medium

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9762. Find z to two decimals.

A = 0.9762

z =

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 5% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points5%

x = points

6.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 10% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g10%

x = g

Answer key

1. z = 1.75
2. σ = 0.5 mm
3. P = 0.9332
4. z = 2.26
5. x = 124.6 points
6. x = 256.4 g

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