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
−3−2−10123zshaded area to the left of z = 0.0307

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0307. Find z to two decimals.

A = 0.0307
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.0823

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0823. Find z to two decimals.

A = 0.0823
z =
4.Medium
482560P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 482 and 560 h? Give P as a decimal.

μ = 500σ = 40x1 = 482x2 = 560
P =
5.Hard
557085100115130145pointstop 70%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 70% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points70%
x = points
6.Hard
μ = 100x = ?95%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 95% of them lie (the 95th percentile).

μ = 100σ = 15P = 95%
x = points

Answer key

  1. 1. σ = 2.5 min
  2. 2. z = −1.87
  3. 3. z = 1.39
  4. 4. P = 0.6068
  5. 5. x = 92.2 points
  6. 6. x = 124.7 points

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