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
−3−2−10123zshaded area to the left of z = 0.9693

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9693. Find z to two decimals.

A = 0.9693
z =
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
100103P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 100 and 103 points? Give P as a decimal.

μ = 100σ = 15x1 = 100x2 = 103
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0170

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0170. Find z to two decimals.

A = 0.0170
z =
5.Hard
0.04 mm0D − d?

Hole diameters D are normal with mean 25.04 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 = 25.04 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =
6.Hard
μ = 178x = ?95%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 95% of them lie (the 95th percentile).

μ = 178σ = 7P = 95%
x = cm

Answer key

  1. 1. z = 1.87
  2. 2. σ = 9.849 g
  3. 3. P = 0.07926
  4. 4. z = 2.12
  5. 5. P = 0.9633
  6. 6. x = 189.5 cm

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