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
−8 minσ = ?X − Y

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
242.5260.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 242.5 and 260.25 g? Give P as a decimal.

μ = 250σ = 5x1 = 242.5x2 = 260.25
P =
4.Medium
32 min37 minX + Y?

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 37 min. Round z to two decimals.

μX = 12, σX = 1.5μY = 20, σY = 2X + Y > 37 min
P =
5.Hard
157164171178185192199cmtop 85%

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 85% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm85%
x = cm
6.Hard
35455565758595pointstop 30%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 30% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points30%
x = points

Answer key

  1. 1. σ = 9.849 g
  2. 2. σ = 2.5 min
  3. 3. P = 0.913
  4. 4. P = 0.02275
  5. 5. x = 170.7 cm
  6. 6. x = 70.2 points

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