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
μ = 10094P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 94 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 94
P(X < x) =
2.Easy
μ = 6557.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is above 57.5 points? Find P(X > x) as a decimal.

μ = 65σ = 10x = 57.5
P(X > x) =
3.Medium
−3−2−10123zshaded area between −z and z = 0.7063

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7063. Find z to two decimals.

A = 0.7063
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9011

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9011. Find z to two decimals.

A = 0.9011
z =
5.Hard
235240245250255260265gtop 85%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 85% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g85%
x = g
6.Hard
157164171178185192199cmtop 20%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 20% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm20%
x = cm

Answer key

  1. 1. P(X < x) = 0.3446
  2. 2. P(X > x) = 0.7734
  3. 3. z = 1.05
  4. 4. z = 1.65
  5. 5. x = 244.8 g
  6. 6. x = 183.9 cm

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