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 below 255.25 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 255.25

P(X < x) =

2.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

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.1271. Find z to two decimals.

A = 0.1271

z =

4.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 762.3 g. Round z to two decimals.

μ_X = 250, σ_X = 4μ_Y = 500, σ_Y = 9X + Y > 762.3 g

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 bottom 10% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h10%

x = h

6.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 90% of them lie (the 90th percentile).

μ = 178σ = 7P = 90%

x = cm

Answer key

1. P(X < x) = 0.8531
2. σ = 9.849 g
3. z = 1.14
4. P = 0.1056
5. x = 449 h
6. x = 187 cm

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