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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 41 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 41

P(X < x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7157. Find z to two decimals.

A = 0.7157

z =

3.Medium

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 5 of them exceeds 57.3 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 5> 57.3 kg

P =

4.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 100.75 and 118.75 points? Give P as a decimal.

μ = 100σ = 15x₁ = 100.75x₂ = 118.75

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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded bottom 5% is to the left of it. Find the cut-off x.

μ = 100 pointsσ = 15 points5%

x = points

Answer key

1. P(X < x) = 0.9332
2. z = 0.57
3. P = 0.9345
4. P = 0.3744
5. P = 0.7389
6. x = 75.4 points

Full step-by-step solutions: practise this topic on examproblems.com.