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
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
2.Easy
−3−2−10123zshaded area to the left of z = 0.0526

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0526. Find z to two decimals.

A = 0.0526
z =
3.Medium
76103.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 76 and 103.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 76x2 = 103.75
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.9834

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9834. Find z to two decimals.

A = 0.9834
z =
5.Hard
μ = 100x = ?20%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 20% of them lie (the 20th percentile).

μ = 100σ = 15P = 20%
x = points
6.Hard
235240245250255260265gbottom 95%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded bottom 95% is to the left of it. Find the cut-off x.

μ = 250 gσ = 5 g95%
x = g

Answer key

  1. 1. σ = 0.5 mm
  2. 2. z = −1.62
  3. 3. P = 0.5439
  4. 4. z = −2.13
  5. 5. x = 87.38 points
  6. 6. x = 258.2 g

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