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 = 10085P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 85 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 85
P(X < x) =
2.Easy
μ = 10077.5P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 77.5 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 77.5
P(X > x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.0188

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0188. Find z to two decimals.

A = 0.0188
z =
4.Medium
−3−2−10123zshaded area to the right of z = 0.7704

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.7704. Find z to two decimals.

A = 0.7704
z =
5.Hard
μ = 32x = ?97.5%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 32σ = 6P = 97.5%
x = min
6.Hard
235240245250255260265gtop 15%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 15% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g15%
x = g

Answer key

  1. 1. P(X < x) = 0.1587
  2. 2. P(X > x) = 0.9332
  3. 3. z = 2.08
  4. 4. z = −0.74
  5. 5. x = 43.76 min
  6. 6. x = 255.2 g

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