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

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is above 255 g? Find P(X > x) as a decimal.

μ = 250σ = 5x = 255

P(X > x) =

2.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 =

3.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 8 of them exceeds 97.1 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 8> 97.1 kg

P =

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 is below 105.6 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 9< 105.6 kg

P =

5.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 40% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm40%

x = cm

6.Hard

Hole diameters D are normal with mean 25.04 mm and standard deviation 0.02 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.04 mm, σ = 0.02 mmshaft: μ = 25 mm, σ = 0.015 mm

P =

Answer key

1. P(X > x) = 0.1587
2. z = −0.88
3. P = 0.3121
4. P = 0.1587
5. x = 179.8 cm
6. P = 0.9452

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