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 = 0.0409

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0409. Find z to two decimals.

A = 0.0409
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.1093

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1093. Find z to two decimals.

A = 0.1093
z =
3.Medium
65.585P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 65.5 and 85 points? Give P as a decimal.

μ = 65σ = 10x1 = 65.5x2 = 85
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.4713

Drag z so that the shaded area between −z and z under the standard normal curve is 0.4713. Find z to two decimals.

A = 0.4713
z =
5.Hard
235240245250255260265gtop 15%

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

μ = 250 gσ = 5 g15%
x = g
6.Hard
μ = 500x = ?20%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 20% of them lie (the 20th percentile).

μ = 500σ = 40P = 20%
x = h

Answer key

  1. 1. z = −1.74
  2. 2. z = −1.23
  3. 3. P = 0.4573
  4. 4. z = 0.63
  5. 5. x = 255.2 g
  6. 6. x = 466.3 h

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