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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 85 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 85

P(X > x) =

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

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 34 min. Round z to two decimals.

μ_X = 12, σ_X = 1.5μ_Y = 20, σ_Y = 2X + Y > 34 min

P =

4.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 240 and 259.25 g? Give P as a decimal.

μ = 250σ = 5x₁ = 240x₂ = 259.25

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 60% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h60%

x = h

6.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 90% of them lie (the 90th percentile).

μ = 500σ = 40P = 90%

x = h

Answer key

1. P(X > x) = 0.8413
2. σ = 0.5 mm
3. P = 0.2119
4. P = 0.9451
5. x = 490 h
6. x = 551.3 h

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