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 = 0.0244

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0244. Find z to two decimals.

A = 0.0244
z =
2.Easy
−8 minσ = ?X − Y

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 standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
93.25103P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 93.25 and 103 points? Give P as a decimal.

μ = 100σ = 15x1 = 93.25x2 = 103
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.8444

Drag z so that the shaded area between −z and z under the standard normal curve is 0.8444. Find z to two decimals.

A = 0.8444
z =
5.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.01 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.03 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.01 mm
P =
6.Hard
380420460500540580620hbottom 40%

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

μ = 500 hσ = 40 h40%
x = h

Answer key

  1. 1. z = −1.97
  2. 2. σ = 2.5 min
  3. 3. P = 0.2529
  4. 4. z = 1.42
  5. 5. P = 0.9515
  6. 6. x = 490 h

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