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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Name: ____________________   Date: ____________

1.Easy
μ = 178181.85P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 181.85 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 181.85
P(X > x) =
2.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
3.Medium
48 kg51.2 kgT = X₁ + … + X₄?

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 4 of them exceeds 51.2 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 4> 51.2 kg
P =
4.Medium
5773P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 57 and 73 points? Give P as a decimal.

μ = 65σ = 10x1 = 57x2 = 73
P =
5.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 0.01 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 = 0.01 mm
P =
6.Hard
4 s0X − Y?

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 52 s, σX = 4 sμY = 48 s, σY = 3 s
P =

Answer key

  1. 1. P(X > x) = 0.2912
  2. 2. σ = 2.5 min
  3. 3. P = 0.02275
  4. 4. P = 0.5763
  5. 5. P = 0.9868
  6. 6. P = 0.7881

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