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
−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
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
105 s114.6 sX + Y?

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 114.6 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 114.6 s
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0643

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0643. Find z to two decimals.

A = 0.0643
z =
5.Hard
μ = 65x = ?20%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 20% of them lie (the 20th percentile).

μ = 65σ = 10P = 20%
x = points
6.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.02 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 = 0.02 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. σ = 2.5 min
  2. 2. σ = 0.5 mm
  3. 3. P = 0.06681
  4. 4. z = 1.52
  5. 5. x = 56.58 points
  6. 6. P = 0.8554

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