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 0.9265. Find z to two decimals.

A = 0.9265

z =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2643. Find z to two decimals.

A = 0.2643

z =

3.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 27.5 and 41.3 min? Give P as a decimal.

μ = 32σ = 6x₁ = 27.5x₂ = 41.3

P =

4.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 242.75 and 260.25 g? Give P as a decimal.

μ = 250σ = 5x₁ = 242.75x₂ = 260.25

P =

5.Hard

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.015 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 = 25.03 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.02 mm

P =

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 70% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points70%

x = points

Answer key

1. z = 1.45
2. z = −0.63
3. P = 0.7128
4. P = 0.9063
5. P = 0.8849
6. x = 70.2 points

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