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
32 minσ = ?X + Y

X and Y are independent normal variables for the time for two consecutive process steps: X has mean 12 min and standard deviation 1.5 min, Y has mean 20 min and standard deviation 2 min. Find the standard deviation σ of 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
169.6192P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 169.6 and 192 cm? Give P as a decimal.

μ = 178σ = 7x1 = 169.6x2 = 192
P =
4.Medium
144 kg149.5 kgT = X₁ + … + X₁₂?

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 12 of them is below 149.5 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 12< 149.5 kg
P =
5.Hard
10 g0X − Y?

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 500 g, σX = 8 gμY = 490 g, σY = 6 g
P =
6.Hard
μ = 100x = ?75%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 75% of them lie (the 75th percentile).

μ = 100σ = 15P = 75%
x = points

Answer key

  1. 1. σ = 2.5 min
  2. 2. σ = 0.5 mm
  3. 3. P = 0.8622
  4. 4. P = 0.9761
  5. 5. P = 0.8413
  6. 6. x = 110.1 points

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