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 = 0.2643

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2643. Find z to two decimals.

A = 0.2643
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9798

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9798. Find z to two decimals.

A = 0.9798
z =
3.Medium
4570P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 45 and 70 points? Give P as a decimal.

μ = 65σ = 10x1 = 45x2 = 70
P =
4.Medium
2942.8P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 29 and 42.8 min? Give P as a decimal.

μ = 32σ = 6x1 = 29x2 = 42.8
P =
5.Hard
μ = 100x = ?95%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 95% of them lie (the 95th percentile).

μ = 100σ = 15P = 95%
x = points
6.Hard
157164171178185192199cmbottom 30%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded bottom 30% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm30%
x = cm

Answer key

  1. 1. z = −0.63
  2. 2. z = 2.05
  3. 3. P = 0.6687
  4. 4. P = 0.6555
  5. 5. x = 124.7 points
  6. 6. x = 174.4 cm

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