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 is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

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

σ = g

2.Easy

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of 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 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the probability P that X + Y is more than 762.3 g. Round z to two decimals.

μ_X = 250, σ_X = 4μ_Y = 500, σ_Y = 9X + Y > 762.3 g

P =

4.Medium

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9762. Find z to two decimals.

A = 0.9762

z =

5.Hard

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 5% of them lie (the 5th percentile).

μ = 32σ = 6P = 5%

x = min

6.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 75% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h75%

x = h

Answer key

1. σ = 9.849 g
2. σ = 0.5 mm
3. P = 0.1056
4. z = 2.26
5. x = 22.13 min
6. x = 473 h

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