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.

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1.Easy
200 mmσ = ?X + Y

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
2.Easy
40 mmσ = ?X − Y

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of the difference X − Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
3.Medium
−3−2−10123zshaded area to the right of z = 0.9693

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9693. Find z to two decimals.

A = 0.9693
z =
4.Medium
−3−2−10123zshaded area to the right of z = 0.3783

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.3783. Find z to two decimals.

A = 0.3783
z =
5.Hard
μ = 65x = ?80%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 80% of them lie (the 80th percentile).

μ = 65σ = 10P = 80%
x = points
6.Hard
μ = 250x = ?10%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 10% of them lie (the 10th percentile).

μ = 250σ = 5P = 10%
x = g

Answer key

  1. 1. σ = 0.5 mm
  2. 2. σ = 0.5 mm
  3. 3. z = −1.87
  4. 4. z = 0.31
  5. 5. x = 73.42 points
  6. 6. x = 243.6 g

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