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 above 468 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 468

P(X > x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1949. Find z to two decimals.

A = 0.1949

z =

3.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 88 and 123.25 points? Give P as a decimal.

μ = 100σ = 15x₁ = 88x₂ = 123.25

P =

4.Medium

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 5 of them exceeds 205.4 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 5> 205.4 g

P =

5.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 =

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 85% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points85%

x = points

Answer key

1. P(X > x) = 0.7881
2. z = −0.86
3. P = 0.7276
4. P = 0.02222
5. P = 0.8413
6. x = 54.6 points

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