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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3372. Find z to two decimals.

A = 0.3372

z =

2.Easy

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 255.25 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 255.25

P(X < x) =

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 200.5 mm. Round z to two decimals.

μ_X = 120, σ_X = 0.3μ_Y = 80, σ_Y = 0.4X + Y > 200.5 mm

P =

4.Medium

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5346. Find z to two decimals.

A = 0.5346

z =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 10% of them lie (the 10th percentile).

μ = 500σ = 40P = 10%

x = h

6.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 =

Answer key

1. z = −0.42
2. P(X < x) = 0.8531
3. P = 0.1587
4. z = 0.73
5. x = 448.7 h
6. P = 0.8413

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