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
−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
2.Easy
750 gσ = ?X + Y

X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
3.Medium
−3−2−10123zshaded area to the right of z = 0.0244

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0244. Find z to two decimals.

A = 0.0244
z =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0708

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0708. Find z to two decimals.

A = 0.0708
z =
5.Hard
235240245250255260265gbottom 85%

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

μ = 250 gσ = 5 g85%
x = g
6.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

Answer key

  1. 1. σ = 2.5 min
  2. 2. σ = 9.849 g
  3. 3. z = 1.97
  4. 4. z = 1.47
  5. 5. x = 255.2 g
  6. 6. x = 62.5 points

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