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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Name: ____________________ Date: ____________

1.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1894. Find z to two decimals.

A = 0.1894

z =

2.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 175.2 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 175.2

P(X < x) =

3.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 53 and 67.5 points? Give P as a decimal.

μ = 65σ = 10x₁ = 53x₂ = 67.5

P =

4.Medium

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 9 of them exceeds 783 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 9> 783 kg

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 0.02 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 = 0.02 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 bottom 70% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h70%

x = h

Answer key

1. z = −0.88
2. P(X < x) = 0.3446
3. P = 0.4836
4. P = 0.3085
5. P = 0.9616
6. x = 521 h

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