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 = 0.2451

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2451. Find z to two decimals.

A = 0.2451
z =
2.Easy
μ = 100130.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 130.75 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 130.75
P(X < x) =
3.Medium
32 min33.3 minX + 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 probability P that X + Y is more than 33.3 min. Round z to two decimals.

μX = 12, σX = 1.5μY = 20, σY = 2X + Y > 33.3 min
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.7887

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7887. Find z to two decimals.

A = 0.7887
z =
5.Hard
μ = 250x = ?20%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 20% of them lie (the 20th percentile).

μ = 250σ = 5P = 20%
x = g
6.Hard
557085100115130145pointstop 90%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 90% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points90%
x = points

Answer key

  1. 1. z = −0.69
  2. 2. P(X < x) = 0.9798
  3. 3. P = 0.3015
  4. 4. z = 1.25
  5. 5. x = 245.8 g
  6. 6. x = 80.8 points

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