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 heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 181.5 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 181.5

P(X > x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0212. Find z to two decimals.

A = 0.0212

z =

3.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 20.3 and 39.5 min? Give P as a decimal.

μ = 32σ = 6x₁ = 20.3x₂ = 39.5

P =

4.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 247.5 and 252.75 g? Give P as a decimal.

μ = 250σ = 5x₁ = 247.5x₂ = 252.75

P =

5.Hard

Hole diameters D are normal with mean 25.05 mm and standard deviation 0.02 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.01 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.05 mm, σ = 0.02 mmshaft: μ = 25 mm, σ = 0.01 mm

P =

6.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

Answer key

1. P(X > x) = 0.3085
2. z = −2.03
3. P = 0.8688
4. P = 0.4003
5. P = 0.9875
6. x = 566 h

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