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
32 minσ = ?X + Y

X and Y are independent normal variables for the time for two consecutive process steps: X has mean 12 min and standard deviation 1.5 min, Y has mean 20 min and standard deviation 2 min. Find the standard deviation σ of X + Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
2.Easy
μ = 3241.3P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 41.3 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 41.3
P(X > x) =
3.Medium
−3−2−10123zshaded area between −z and z = 0.8836

Drag z so that the shaded area between −z and z under the standard normal curve is 0.8836. Find z to two decimals.

A = 0.8836
z =
4.Medium
−3−2−10123zshaded area to the right of z = 0.3707

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.3707. Find z to two decimals.

A = 0.3707
z =
5.Hard
μ = 500x = ?10%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 10% of them lie (the 10th percentile).

μ = 500σ = 40P = 10%
x = h
6.Hard
557085100115130145pointsbottom 20%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded bottom 20% is to the left of it. Find the cut-off x.

μ = 100 pointsσ = 15 points20%
x = points

Answer key

  1. 1. σ = 2.5 min
  2. 2. P(X > x) = 0.06057
  3. 3. z = 1.57
  4. 4. z = 0.33
  5. 5. x = 448.7 h
  6. 6. x = 87.4 points

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