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
−3−2−10123zshaded area to the left of z = 0.7291

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7291. Find z to two decimals.

A = 0.7291
z =
2.Easy
200 mmσ = ?X + Y

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
3.Medium
−3−2−10123zshaded area between −z and z = 0.7887

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7887. Find z to two decimals.

A = 0.7887
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.6102

Drag z so that the shaded area between −z and z under the standard normal curve is 0.6102. Find z to two decimals.

A = 0.6102
z =
5.Hard
157164171178185192199cmbottom 20%

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 20% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm20%
x = cm
6.Hard
380420460500540580620htop 15%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 15% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h15%
x = h

Answer key

  1. 1. z = 0.61
  2. 2. σ = 0.5 mm
  3. 3. z = 1.25
  4. 4. z = 0.86
  5. 5. x = 172.1 cm
  6. 6. x = 542 h

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