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
750 gσ = ?X + Y

X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of 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 kg1041 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 exceeds 1041 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 12> 1041 kg
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.8438

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8438. Find z to two decimals.

A = 0.8438
z =
5.Hard
μ = 100x = ?5%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 5% of them lie (the 5th percentile).

μ = 100σ = 15P = 5%
x = points
6.Hard
0.05 mm0D − d?

Hole diameters D are normal with mean 25.05 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 = 25.05 mm, σ = 0.02 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. σ = 9.849 g
  2. 2. σ = 2.5 min
  3. 3. P = 0.3085
  4. 4. z = −1.01
  5. 5. x = 75.33 points
  6. 6. P = 0.9616

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