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
750 gσ = ?X + Y

X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
2.Easy
μ = 3235.3P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 35.3 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 35.3
P(X > x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.0359

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0359. Find z to two decimals.

A = 0.0359
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.5407

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5407. Find z to two decimals.

A = 0.5407
z =
5.Hard
157164171178185192199cmbottom 60%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded bottom 60% is to the left of it. Find the cut-off x.

μ = 178 cmσ = 7 cm60%
x = cm
6.Hard
μ = 100x = ?25%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 25% of them lie (the 25th percentile).

μ = 100σ = 15P = 25%
x = points

Answer key

  1. 1. σ = 9.849 g
  2. 2. P(X > x) = 0.2912
  3. 3. z = 1.8
  4. 4. z = 0.74
  5. 5. x = 179.8 cm
  6. 6. x = 89.88 points

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