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 = 3233.5P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 33.5 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 33.5
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 s95.4 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 95.4 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 95.4 s
P =
4.Medium
100 kg98.5 kgT = X₁ + … + X₄?

The masses of bags of cement are independent and normal with mean 25 kg and standard deviation 0.5 kg. Find the probability P that the total mass of 4 of them is below 98.5 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 4< 98.5 kg
P =
5.Hard
380420460500540580620htop 25%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 25% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h25%
x = h
6.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.01 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 = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. P(X < x) = 0.5987
  2. 2. σ = 2.5 min
  3. 3. P = 0.9332
  4. 4. P = 0.06681
  5. 5. x = 527 h
  6. 6. P = 0.8133

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