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 0.8599. Find z to two decimals.

A = 0.8599

z =

2.Easy

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of the difference X − Y.

μ_X = 120 mm, σ_X = 0.3 mmμ_Y = 80 mm, σ_Y = 0.4 mm

σ = mm

3.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 20 and 39.2 min? Give P as a decimal.

μ = 32σ = 6x₁ = 20x₂ = 39.2

P =

4.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 53.5 and 83 points? Give P as a decimal.

μ = 65σ = 10x₁ = 53.5x₂ = 83

P =

5.Hard

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 10% of them lie (the 10th percentile).

μ = 32σ = 6P = 10%

x = min

6.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 =

Answer key

1. z = 1.08
2. σ = 0.5 mm
3. P = 0.8622
4. P = 0.839
5. x = 24.31 min
6. P = 0.9616

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