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 above 248.25 g? Find P(X > x) as a decimal.

μ = 250σ = 5x = 248.25

P(X > x) =

2.Easy

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 standard deviation σ of the difference X − Y.

μ_X = 12 min, σ_X = 1.5 minμ_Y = 20 min, σ_Y = 2 min

σ = min

3.Medium

Drag z so that the shaded area between −z and z under the standard normal curve is 0.3182. Find z to two decimals.

A = 0.3182

z =

4.Medium

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 9 of them exceeds 109.2 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 9> 109.2 kg

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 5% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h5%

x = h

6.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

Answer key

1. P(X > x) = 0.6368
2. σ = 2.5 min
3. z = 0.41
4. P = 0.3085
5. x = 566 h
6. x = 124.6 points

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