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 = 500428P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 428 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 428
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9750

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9750. Find z to two decimals.

A = 0.9750
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.9515

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9515. Find z to two decimals.

A = 0.9515
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.4778

Drag z so that the shaded area between −z and z under the standard normal curve is 0.4778. Find z to two decimals.

A = 0.4778
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
10 cm0X − Y?

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 180 cm, σX = 10 cmμY = 170 cm, σY = 12 cm
P =

Answer key

  1. 1. P(X > x) = 0.9641
  2. 2. z = 1.96
  3. 3. z = −1.66
  4. 4. z = 0.64
  5. 5. x = 179.8 cm
  6. 6. P = 0.7389

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