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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Name: ____________________ Date: ____________

1.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0793. Find z to two decimals.

A = 0.0793

z =

2.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

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 740.2 g. Round z to two decimals.

μ_X = 250, σ_X = 4μ_Y = 500, σ_Y = 9X + Y > 740.2 g

P =

4.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 20 and 35.3 min? Give P as a decimal.

μ = 32σ = 6x₁ = 20x₂ = 35.3

P =

5.Hard

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 180 cm, σ_X = 10 cmμ_Y = 170 cm, σ_Y = 12 cm

P =

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 90% of them lie (the 90th percentile).

μ = 65σ = 10P = 90%

x = points

Answer key

1. z = −1.41
2. σ = 2.5 min
3. P = 0.8413
4. P = 0.6861
5. P = 0.7389
6. x = 77.82 points

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