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
−3−2−10123zshaded area to the left of z = 0.8810

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8810. Find z to two decimals.

A = 0.8810
z =
3.Medium
−3−2−10123zshaded area between −z and z = 0.7330

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7330. Find z to two decimals.

A = 0.7330
z =
4.Medium
55.580.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 55.5 and 80.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 55.5x2 = 80.5
P =
5.Hard
157164171178185192199cmbottom 80%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded bottom 80% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm80%
x = cm
6.Hard
235240245250255260265gbottom 15%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded bottom 15% is to the left of it. Find the cut-off x.

μ = 250 gσ = 5 g15%
x = g

Answer key

  1. 1. σ = 9.849 g
  2. 2. z = 1.18
  3. 3. z = 1.11
  4. 4. P = 0.7684
  5. 5. x = 183.9 cm
  6. 6. x = 244.8 g

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