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 = 178188.5P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 188.5 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 188.5
P(X < x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.0166

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0166. Find z to two decimals.

A = 0.0166
z =
3.Medium
247.75257.75P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 247.75 and 257.75 g? Give P as a decimal.

μ = 250σ = 5x1 = 247.75x2 = 257.75
P =
4.Medium
96.25115.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 96.25 and 115.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 96.25x2 = 115.75
P =
5.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
6.Hard
35455565758595pointsbottom 10%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 10% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points10%
x = points

Answer key

  1. 1. P(X < x) = 0.9332
  2. 2. z = −2.13
  3. 3. P = 0.6131
  4. 4. P = 0.4518
  5. 5. x = 124.7 points
  6. 6. x = 52.2 points

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