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
−3−2−10123zshaded area to the left of z = 0.7995

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7995. Find z to two decimals.

A = 0.7995
z =
3.Medium
100118P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 100 and 118 points? Give P as a decimal.

μ = 100σ = 15x1 = 100x2 = 118
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.7457

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7457. Find z to two decimals.

A = 0.7457
z =
5.Hard
235240245250255260265gbottom 90%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded bottom 90% is to the left of it. Find the cut-off x.

μ = 250 gσ = 5 g90%
x = g
6.Hard
380420460500540580620hbottom 70%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded bottom 70% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h70%
x = h

Answer key

  1. 1. σ = 9.849 g
  2. 2. z = 0.84
  3. 3. P = 0.3849
  4. 4. z = 1.14
  5. 5. x = 256.4 g
  6. 6. x = 521 h

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