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 0.7389. Find z to two decimals.

A = 0.7389

z =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1190. Find z to two decimals.

A = 0.1190

z =

3.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 55.5 and 83 points? Give P as a decimal.

μ = 65σ = 10x₁ = 55.5x₂ = 83

P =

4.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 470 and 542 h? Give P as a decimal.

μ = 500σ = 40x₁ = 470x₂ = 542

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

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. z = 0.64
2. z = −1.18
3. P = 0.793
4. P = 0.6265
5. P = 0.7389
6. P = 0.7881

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