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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1.Easy

X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.

μ_X = 250 g, σ_X = 4 gμ_Y = 500 g, σ_Y = 9 g

σ = g

2.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 186.75 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 186.75

P(X > x) =

3.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 500 and 534 h? Give P as a decimal.

μ = 500σ = 40x₁ = 500x₂ = 534

P =

4.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 62 and 73.5 points? Give P as a decimal.

μ = 65σ = 10x₁ = 62x₂ = 73.5

P =

5.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 85% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points85%

x = points

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 100σ = 15P = 99%

x = points

Answer key

1. σ = 9.849 g
2. P(X > x) = 0.1056
3. P = 0.3023
4. P = 0.4202
5. x = 75.4 points
6. x = 134.9 points

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