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 = 0.8133

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8133. Find z to two decimals.

A = 0.8133
z =
2.Easy
200 mmσ = ?X + Y

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
3.Medium
2633.5P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 26 and 33.5 min? Give P as a decimal.

μ = 32σ = 6x1 = 26x2 = 33.5
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.6102

Drag z so that the shaded area between −z and z under the standard normal curve is 0.6102. Find z to two decimals.

A = 0.6102
z =
5.Hard
0.04 mm0D − d?

Hole diameters D are normal with mean 25.04 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.04 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.01 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 = 0.01 mmshaft: μ = 25 mm, σ = 0.01 mm
P =

Answer key

  1. 1. z = 0.89
  2. 2. σ = 0.5 mm
  3. 3. P = 0.4401
  4. 4. z = 0.86
  5. 5. P = 0.9868
  6. 6. P = 0.983

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