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 = 0.1251

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1251. Find z to two decimals.

A = 0.1251
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.7054

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7054. Find z to two decimals.

A = 0.7054
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.9049

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9049. Find z to two decimals.

A = 0.9049
z =
4.Medium
49.583.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 49.5 and 83.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 49.5x2 = 83.5
P =
5.Hard
0.05 mm0D − d?

Hole diameters D are normal with mean 25.05 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 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 = 0.015 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.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 =

Answer key

  1. 1. z = −1.15
  2. 2. z = 0.54
  3. 3. z = −1.31
  4. 4. P = 0.9073
  5. 5. P = 0.9909
  6. 6. P = 0.8413

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