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 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 standard deviation σ of the difference X − Y.

μ_X = 120 mm, σ_X = 0.3 mmμ_Y = 80 mm, σ_Y = 0.4 mm

σ = mm

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8907. Find z to two decimals.

A = 0.8907

z =

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9772. Find z to two decimals.

A = 0.9772

z =

4.Medium

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 12 of them exceeds 957.6 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 12> 957.6 kg

P =

5.Hard

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 500 g, σ_X = 8 gμ_Y = 490 g, σ_Y = 6 g

P =

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 = 0.5 mm
2. z = 1.23
3. z = −2
4. P = 0.9332
5. P = 0.8413
6. P = 0.7881

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