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
μ = 100122.5P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 122.5 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 122.5
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.1170

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1170. Find z to two decimals.

A = 0.1170
z =
3.Medium
−3−2−10123zshaded area between −z and z = 0.7959

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7959. Find z to two decimals.

A = 0.7959
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.2737

Drag z so that the shaded area between −z and z under the standard normal curve is 0.2737. Find z to two decimals.

A = 0.2737
z =
5.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.02 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.03 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.02 mm
P =
6.Hard
μ = 100x = ?5%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 5% of them lie (the 5th percentile).

μ = 100σ = 15P = 5%
x = points

Answer key

  1. 1. P(X > x) = 0.06681
  2. 2. z = −1.19
  3. 3. z = 1.27
  4. 4. z = 0.35
  5. 5. P = 0.8849
  6. 6. x = 75.33 points

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