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 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the standard deviation σ of the difference X − Y.

μ_X = 12 min, σ_X = 1.5 minμ_Y = 20 min, σ_Y = 2 min

σ = min

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0322. Find z to two decimals.

A = 0.0322

z =

3.Medium

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 probability P that X + Y is more than 200.8 mm. Round z to two decimals.

μ_X = 120, σ_X = 0.3μ_Y = 80, σ_Y = 0.4X + Y > 200.8 mm

P =

4.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9864. Find z to two decimals.

A = 0.9864

z =

5.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 90% of them lie (the 90th percentile).

μ = 250σ = 5P = 90%

x = g

6.Hard

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 52 s, σ_X = 4 sμ_Y = 48 s, σ_Y = 3 s

P =

Answer key

1. σ = 2.5 min
2. z = −1.85
3. P = 0.0548
4. z = −2.21
5. x = 256.4 g
6. P = 0.7881

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