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
μ = 6581.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is above 81.5 points? Find P(X > x) as a decimal.

μ = 65σ = 10x = 81.5
P(X > x) =
2.Easy
μ = 3229.9P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 29.9 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 29.9
P(X < x) =
3.Medium
105 s95.4 sX + Y?

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 95.4 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 95.4 s
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.6629

Drag z so that the shaded area between −z and z under the standard normal curve is 0.6629. Find z to two decimals.

A = 0.6629
z =
5.Hard
μ = 32x = ?75%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 75% of them lie (the 75th percentile).

μ = 32σ = 6P = 75%
x = min
6.Hard
157164171178185192199cmtop 15%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 15% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm15%
x = cm

Answer key

  1. 1. P(X > x) = 0.04947
  2. 2. P(X < x) = 0.3632
  3. 3. P = 0.9332
  4. 4. z = 0.96
  5. 5. x = 36.05 min
  6. 6. x = 185.3 cm

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