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 = 0.3121

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3121. Find z to two decimals.

A = 0.3121
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.6255

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.6255. Find z to two decimals.

A = 0.6255
z =
3.Medium
32 min33.3 minX + 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 probability P that X + Y is more than 33.3 min. Round z to two decimals.

μX = 12, σX = 1.5μY = 20, σY = 2X + Y > 33.3 min
P =
4.Medium
60.575P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 60.5 and 75 points? Give P as a decimal.

μ = 65σ = 10x1 = 60.5x2 = 75
P =
5.Hard
235240245250255260265gtop 15%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 15% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g15%
x = g
6.Hard
μ = 100x = ?90%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 90% of them lie (the 90th percentile).

μ = 100σ = 15P = 90%
x = points

Answer key

  1. 1. z = −0.49
  2. 2. z = 0.32
  3. 3. P = 0.3015
  4. 4. P = 0.515
  5. 5. x = 255.2 g
  6. 6. x = 119.2 points

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