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 battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is below 564 h? Find P(X < x) as a decimal.

μ = 500σ = 40x = 564

P(X < x) =

2.Easy

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 259.25 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 259.25

P(X < x) =

3.Medium

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 242 and 255 g? Give P as a decimal.

μ = 250σ = 5x₁ = 242x₂ = 255

P =

4.Medium

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 probability P that X + Y is more than 29.5 min. Round z to two decimals.

μ_X = 12, σ_X = 1.5μ_Y = 20, σ_Y = 2X + Y > 29.5 min

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 20% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h20%

x = h

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. P(X < x) = 0.9452
2. P(X < x) = 0.9678
3. P = 0.7865
4. P = 0.8413
5. x = 534 h
6. P = 0.7881

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