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 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

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

σ = g

2.Easy

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 73 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 73

P(X > x) =

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8389. Find z to two decimals.

A = 0.8389

z =

4.Medium

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5587. Find z to two decimals.

A = 0.5587

z =

5.Hard

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 500 g, σ_X = 8 gμ_Y = 490 g, σ_Y = 6 g

P =

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 60% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points60%

x = points

Answer key

1. σ = 9.849 g
2. P(X > x) = 0.9641
3. z = −0.99
4. z = 0.77
5. P = 0.8413
6. x = 67.5 points

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