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 = 0.3594

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3594. Find z to two decimals.

A = 0.3594
z =
2.Easy
μ = 178188.85P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 188.85 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 188.85
P(X > x) =
3.Medium
105 s101.8 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 101.8 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 101.8 s
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.5705

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5705. Find z to two decimals.

A = 0.5705
z =
5.Hard
μ = 65x = ?75%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 75% of them lie (the 75th percentile).

μ = 65σ = 10P = 75%
x = points
6.Hard
μ = 178x = ?95%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 95% of them lie (the 95th percentile).

μ = 178σ = 7P = 95%
x = cm

Answer key

  1. 1. z = −0.36
  2. 2. P(X > x) = 0.06057
  3. 3. P = 0.6915
  4. 4. z = 0.79
  5. 5. x = 71.75 points
  6. 6. x = 189.5 cm

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