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 battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 542 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 542

P(X > x) =

2.Easy

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 430 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 430

P(X > x) =

3.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 244.25 and 260 g? Give P as a decimal.

μ = 250σ = 5x₁ = 244.25x₂ = 260

P =

4.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 422 and 532 h? Give P as a decimal.

μ = 500σ = 40x₁ = 422x₂ = 532

P =

5.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 0.01 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 = 0.01 mm

P =

6.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 95% of them lie (the 95th percentile).

μ = 250σ = 5P = 95%

x = g

Answer key

1. P(X > x) = 0.1469
2. P(X > x) = 0.9599
3. P = 0.8522
4. P = 0.7626
5. P = 0.9868
6. x = 258.2 g

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