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
−8 minσ = ?X − Y

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
2.Easy
−3−2−10123zshaded area to the left of z = 0.8023

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8023. Find z to two decimals.

A = 0.8023
z =
3.Medium
−3−2−10123zshaded area between −z and z = 0.9488

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9488. Find z to two decimals.

A = 0.9488
z =
4.Medium
5773.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 57 and 73.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 57x2 = 73.5
P =
5.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.015 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 = 25.02 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 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 = 25.02 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. σ = 2.5 min
  2. 2. z = 0.85
  3. 3. z = 1.95
  4. 4. P = 0.5905
  5. 5. P = 0.8264
  6. 6. P = 0.7881

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