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

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 124.75 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 124.75

P(X < x) =

2.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

3.Medium

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 176.25 and 179.4 cm? Give P as a decimal.

μ = 178σ = 7x₁ = 176.25x₂ = 179.4

P =

4.Medium

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 114.6 s. Round z to two decimals.

μ_X = 60, σ_X = 5μ_Y = 45, σ_Y = 4X + Y > 114.6 s

P =

5.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded bottom 75% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm75%

x = cm

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 90% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points90%

x = points

Answer key

1. P(X < x) = 0.9505
2. σ = 9.849 g
3. P = 0.178
4. P = 0.06681
5. x = 182.7 cm
6. x = 80.8 points

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