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
μ = 3244P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 44 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 44
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.3707

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

A = 0.3707
z =
3.Medium
82.75108.25P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 82.75 and 108.25 points? Give P as a decimal.

μ = 100σ = 15x1 = 82.75x2 = 108.25
P =
4.Medium
88.75112.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 88.75 and 112.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 88.75x2 = 112.75
P =
5.Hard
380420460500540580620hbottom 40%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded bottom 40% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h40%
x = h
6.Hard
557085100115130145pointsbottom 80%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded bottom 80% is to the left of it. Find the cut-off x.

μ = 100 pointsσ = 15 points80%
x = points

Answer key

  1. 1. P(X > x) = 0.02275
  2. 2. z = −0.33
  3. 3. P = 0.5838
  4. 4. P = 0.5757
  5. 5. x = 490 h
  6. 6. x = 112.6 points

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