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 = 0.3372

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3372. Find z to two decimals.

A = 0.3372
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9884

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9884. Find z to two decimals.

A = 0.9884
z =
3.Medium
100118.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 100 and 118.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 100x2 = 118.75
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.8508

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8508. Find z to two decimals.

A = 0.8508
z =
5.Hard
35455565758595pointsbottom 10%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded bottom 10% is to the left of it. Find the cut-off x.

μ = 65 pointsσ = 10 points10%
x = points
6.Hard
4 s0X − Y?

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 52 s, σX = 4 sμY = 48 s, σY = 3 s
P =

Answer key

  1. 1. z = −0.42
  2. 2. z = 2.27
  3. 3. P = 0.3944
  4. 4. z = −1.04
  5. 5. x = 52.2 points
  6. 6. P = 0.7881

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