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 = 178171P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 171 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 171
P(X > x) =
2.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) =
3.Medium
−3−2−10123zshaded area between −z and z = 0.9164

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9164. Find z to two decimals.

A = 0.9164
z =
4.Medium
105 s111.4 sX + Y?

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 111.4 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 111.4 s
P =
5.Hard
235240245250255260265gbottom 10%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded bottom 10% is to the left of it. Find the cut-off x.

μ = 250 gσ = 5 g10%
x = g
6.Hard
μ = 65x = ?99%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 65σ = 10P = 99%
x = points

Answer key

  1. 1. P(X > x) = 0.8413
  2. 2. P(X < x) = 0.9332
  3. 3. z = 1.73
  4. 4. P = 0.1587
  5. 5. x = 243.6 g
  6. 6. x = 88.26 points

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