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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1492. Find z to two decimals.

A = 0.1492

z =

3.Medium

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 166.8 and 190.95 cm? Give P as a decimal.

μ = 178σ = 7x₁ = 166.8x₂ = 190.95

P =

4.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 37 min. Round z to two decimals.

μ_X = 12, σ_X = 1.5μ_Y = 20, σ_Y = 2X + Y > 37 min

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 bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 5% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g5%

x = g

Answer key

1. σ = 9.849 g
2. z = −1.04
3. P = 0.913
4. P = 0.02275
5. x = 75.4 points
6. x = 258.2 g

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