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 = 0.7324

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7324. Find z to two decimals.

A = 0.7324
z =
2.Easy
−8 minσ = ?X − Y

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
5777P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 57 and 77 points? Give P as a decimal.

μ = 65σ = 10x1 = 57x2 = 77
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.2810

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.2810. Find z to two decimals.

A = 0.2810
z =
5.Hard
μ = 100x = ?5%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 5% of them lie (the 5th percentile).

μ = 100σ = 15P = 5%
x = points
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 = 0.62
  2. 2. σ = 2.5 min
  3. 3. P = 0.6731
  4. 4. z = 0.58
  5. 5. x = 75.33 points
  6. 6. P = 0.8413

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