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 = 0.0436

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0436. Find z to two decimals.

A = 0.0436
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.0122

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0122. Find z to two decimals.

A = 0.0122
z =
3.Medium
−3−2−10123zshaded area between −z and z = 0.7620

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7620. Find z to two decimals.

A = 0.7620
z =
4.Medium
5785.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 57 and 85.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 57x2 = 85.5
P =
5.Hard
μ = 500x = ?95%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 95% of them lie (the 95th percentile).

μ = 500σ = 40P = 95%
x = h
6.Hard
35455565758595pointsbottom 95%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 95% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points95%
x = points

Answer key

  1. 1. z = −1.71
  2. 2. z = −2.25
  3. 3. z = 1.18
  4. 4. P = 0.768
  5. 5. x = 565.8 h
  6. 6. x = 81.4 points

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