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 = 0.8849

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8849. Find z to two decimals.

A = 0.8849
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9699

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9699. Find z to two decimals.

A = 0.9699
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.9633

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9633. Find z to two decimals.

A = 0.9633
z =
4.Medium
−3−2−10123zshaded area to the right of z = 0.9803

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9803. Find z to two decimals.

A = 0.9803
z =
5.Hard
μ = 65x = ?97.5%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 65σ = 10P = 97.5%
x = points
6.Hard
μ = 500x = ?97.5%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 500σ = 40P = 97.5%
x = h

Answer key

  1. 1. z = 1.2
  2. 2. z = 1.88
  3. 3. z = −1.79
  4. 4. z = −2.06
  5. 5. x = 84.6 points
  6. 6. x = 578.4 h

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