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 0.6736. Find z to two decimals.

A = 0.6736

z =

2.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 175.55 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 175.55

P(X < x) =

3.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 30.5 and 35 min? Give P as a decimal.

μ = 32σ = 6x₁ = 30.5x₂ = 35

P =

4.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 250 and 259.25 g? Give P as a decimal.

μ = 250σ = 5x₁ = 250x₂ = 259.25

P =

5.Hard

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 500 g, σ_X = 8 gμ_Y = 490 g, σ_Y = 6 g

P =

6.Hard

Hole diameters D are normal with mean 25.04 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 = 25.04 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.02 mm

P =

Answer key

1. z = 0.45
2. P(X < x) = 0.3632
3. P = 0.2902
4. P = 0.4678
5. P = 0.8413
6. P = 0.9452

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