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 = 0.9082

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9082. Find z to two decimals.

A = 0.9082
z =
2.Easy
μ = 10082.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 82.75 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 82.75
P(X > x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.7549

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.7549. Find z to two decimals.

A = 0.7549
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9342

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9342. Find z to two decimals.

A = 0.9342
z =
5.Hard
μ = 100x = ?10%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 10% of them lie (the 10th percentile).

μ = 100σ = 15P = 10%
x = points
6.Hard
10 cm0X − Y?

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 180 cm, σX = 10 cmμY = 170 cm, σY = 12 cm
P =

Answer key

  1. 1. z = 1.33
  2. 2. P(X > x) = 0.8749
  3. 3. z = −0.69
  4. 4. z = 1.84
  5. 5. x = 80.78 points
  6. 6. P = 0.7389

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