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
−250 gσ = ?X − Y

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
2.Easy
μ = 250241.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 241.25 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 241.25
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
436580P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 436 and 580 h? Give P as a decimal.

μ = 500σ = 40x1 = 436x2 = 580
P =
5.Hard
35455565758595pointsbottom 40%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 40% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points40%
x = points
6.Hard
157164171178185192199cmtop 70%

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 70% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm70%
x = cm

Answer key

  1. 1. σ = 9.849 g
  2. 2. P(X < x) = 0.04006
  3. 3. z = 1.05
  4. 4. P = 0.9225
  5. 5. x = 62.5 points
  6. 6. x = 174.4 cm

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