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 worksheetPractise 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
−3−2−10123zshaded area to the left of z = 0.0174

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0174. Find z to two decimals.

A = 0.0174
z =
2.Easy
μ = 500440P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is below 440 h? Find P(X < x) as a decimal.

μ = 500σ = 40x = 440
P(X < x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.2578

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.2578. Find z to two decimals.

A = 0.2578
z =
4.Medium
750 g764.8 gX + Y?

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the probability P that X + Y is more than 764.8 g. Round z to two decimals.

μX = 250, σX = 4μY = 500, σY = 9X + Y > 764.8 g
P =
5.Hard
0.04 mm0D − d?

Hole diameters D are normal with mean 25.04 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.04 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.Hard
10 g0X − Y?

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.

μX = 500 g, σX = 8 gμY = 490 g, σY = 6 g
P =

Answer key

  1. 1. z = −2.11
  2. 2. P(X < x) = 0.06681
  3. 3. z = 0.65
  4. 4. P = 0.06681
  5. 5. P = 0.9868
  6. 6. P = 0.8413

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