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
−250 gσ = ?X − Y

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
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
1020 kg1062 kgT = X₁ + … + X₁₂?

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 12 of them is below 1062 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 12< 1062 kg
P =
4.Medium
200 mm199.3 mmX + Y?

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the probability P that X + Y is more than 199.3 mm. Round z to two decimals.

μX = 120, σX = 0.3μY = 80, σY = 0.4X + Y > 199.3 mm
P =
5.Hard
μ = 250x = ?10%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 10% of them lie (the 10th percentile).

μ = 250σ = 5P = 10%
x = g
6.Hard
35455565758595pointstop 30%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 30% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points30%
x = points

Answer key

  1. 1. σ = 9.849 g
  2. 2. σ = 2.5 min
  3. 3. P = 0.8413
  4. 4. P = 0.9192
  5. 5. x = 243.6 g
  6. 6. x = 70.2 points

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