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
200 mmσ = ?X + Y

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
2.Easy
−3−2−10123zshaded area to the left of z = 0.2206

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2206. Find z to two decimals.

A = 0.2206
z =
3.Medium
65.583P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 65.5 and 83 points? Give P as a decimal.

μ = 65σ = 10x1 = 65.5x2 = 83
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0643

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0643. Find z to two decimals.

A = 0.0643
z =
5.Hard
μ = 250x = ?95%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 95% of them lie (the 95th percentile).

μ = 250σ = 5P = 95%
x = g
6.Hard
μ = 100x = ?75%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 75% of them lie (the 75th percentile).

μ = 100σ = 15P = 75%
x = points

Answer key

  1. 1. σ = 0.5 mm
  2. 2. z = −0.77
  3. 3. P = 0.4441
  4. 4. z = 1.52
  5. 5. x = 258.2 g
  6. 6. x = 110.1 points

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