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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Name: ____________________   Date: ____________

1.Easy
−3−2−10123zshaded area to the left of z = 0.6368

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.6368. Find z to two decimals.

A = 0.6368
z =
2.Easy
μ = 6575.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is below 75.5 points? Find P(X < x) as a decimal.

μ = 65σ = 10x = 75.5
P(X < x) =
3.Medium
169.6186.4P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 169.6 and 186.4 cm? Give P as a decimal.

μ = 178σ = 7x1 = 169.6x2 = 186.4
P =
4.Medium
50.580.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 50.5 and 80.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 50.5x2 = 80.5
P =
5.Hard
157164171178185192199cmbottom 20%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded bottom 20% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm20%
x = cm
6.Hard
μ = 32x = ?90%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 90% of them lie (the 90th percentile).

μ = 32σ = 6P = 90%
x = min

Answer key

  1. 1. z = 0.35
  2. 2. P(X < x) = 0.8531
  3. 3. P = 0.7699
  4. 4. P = 0.8659
  5. 5. x = 172.1 cm
  6. 6. x = 39.69 min

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