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 = 6547P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is below 47 points? Find P(X < x) as a decimal.

μ = 65σ = 10x = 47
P(X < x) =
2.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
3.Medium
105 s117.8 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 117.8 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 117.8 s
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.7850

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7850. Find z to two decimals.

A = 0.7850
z =
5.Hard
μ = 250x = ?20%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 20% of them lie (the 20th percentile).

μ = 250σ = 5P = 20%
x = g
6.Hard
0.04 mm0D − d?

Hole diameters D are normal with mean 25.04 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 = 25.04 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. P(X < x) = 0.03593
  2. 2. σ = 2.5 min
  3. 3. P = 0.02275
  4. 4. z = 1.24
  5. 5. x = 245.8 g
  6. 6. P = 0.9452

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