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 = 0.9599

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9599. Find z to two decimals.

A = 0.9599
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9772

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9772. Find z to two decimals.

A = 0.9772
z =
3.Medium
48 kg48.8 kgT = X₁ + … + X₄?

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 4 of them is below 48.8 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 4< 48.8 kg
P =
4.Medium
5383.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 53 and 83.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 53x2 = 83.5
P =
5.Hard
4 s0X − Y?

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 52 s, σX = 4 sμY = 48 s, σY = 3 s
P =
6.Hard
235240245250255260265gtop 90%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 90% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g90%
x = g

Answer key

  1. 1. z = 1.75
  2. 2. z = 2
  3. 3. P = 0.6915
  4. 4. P = 0.8528
  5. 5. P = 0.7881
  6. 6. x = 243.6 g

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