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 = 0.9656

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9656. Find z to two decimals.

A = 0.9656
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.7486

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7486. Find z to two decimals.

A = 0.7486
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.9441

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9441. Find z to two decimals.

A = 0.9441
z =
4.Medium
247.5255P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 247.5 and 255 g? Give P as a decimal.

μ = 250σ = 5x1 = 247.5x2 = 255
P =
5.Hard
μ = 250x = ?75%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 75% of them lie (the 75th percentile).

μ = 250σ = 5P = 75%
x = g
6.Hard
35455565758595pointsbottom 25%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 25% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points25%
x = points

Answer key

  1. 1. z = 1.82
  2. 2. z = 0.67
  3. 3. z = −1.59
  4. 4. P = 0.5328
  5. 5. x = 253.4 g
  6. 6. x = 58.3 points

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