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 = 178171P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 171 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 171
P(X < x) =
2.Easy
μ = 6575P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is above 75 points? Find P(X > x) as a decimal.

μ = 65σ = 10x = 75
P(X > x) =
3.Medium
850 kg812.1 kgT = X₁ + … + X₁₀?

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 10 of them exceeds 812.1 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 10> 812.1 kg
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.8997

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8997. Find z to two decimals.

A = 0.8997
z =
5.Hard
μ = 65x = ?25%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 25% of them lie (the 25th percentile).

μ = 65σ = 10P = 25%
x = points
6.Hard
157164171178185192199cmbottom 80%

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 80% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm80%
x = cm

Answer key

  1. 1. P(X < x) = 0.1587
  2. 2. P(X > x) = 0.1587
  3. 3. P = 0.8413
  4. 4. z = −1.28
  5. 5. x = 58.26 points
  6. 6. x = 183.9 cm

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