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
−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
247.75260.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 247.75 and 260.25 g? Give P as a decimal.

μ = 250σ = 5x1 = 247.75x2 = 260.25
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.8715

Drag z so that the shaded area between −z and z under the standard normal curve is 0.8715. Find z to two decimals.

A = 0.8715
z =
5.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.02 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.02 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =
6.Hard
35455565758595pointsbottom 25%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 25% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points25%
x = points

Answer key

  1. 1. σ = 0.5 mm
  2. 2. σ = 2.5 min
  3. 3. P = 0.6535
  4. 4. z = 1.52
  5. 5. P = 0.8133
  6. 6. x = 58.3 points

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