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
−3−2−10123zshaded area to the left of z = 0.9656

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9656. Find z to two decimals.

A = 0.9656
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
65.573.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 65.5 and 73.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 65.5x2 = 73.5
P =
4.Medium
3241P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 32 and 41 min? Give P as a decimal.

μ = 32σ = 6x1 = 32x2 = 41
P =
5.Hard
μ = 32x = ?10%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 10% of them lie (the 10th percentile).

μ = 32σ = 6P = 10%
x = min
6.Hard
557085100115130145pointstop 30%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 30% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points30%
x = points

Answer key

  1. 1. z = 1.82
  2. 2. σ = 2.5 min
  3. 3. P = 0.2824
  4. 4. P = 0.4332
  5. 5. x = 24.31 min
  6. 6. x = 107.8 points

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