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
40 mmσ = ?X − 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 standard deviation σ of the difference X − Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
2.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
3.Medium
5367.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 53 and 67.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 53x2 = 67.5
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0409

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0409. Find z to two decimals.

A = 0.0409
z =
5.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 =
6.Hard
0.05 mm0D − d?

Hole diameters D are normal with mean 25.05 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 = 25.05 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. σ = 0.5 mm
  2. 2. σ = 9.849 g
  3. 3. P = 0.4836
  4. 4. z = 1.74
  5. 5. P = 0.7881
  6. 6. P = 0.9875

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