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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
−3−2−10123zshaded area to the left of z = 0.9515

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

A = 0.9515
z =
2.Easy
μ = 250251.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 251.25 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 251.25
P(X < x) =
3.Medium
32 min30 minX + Y?

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 30 min. Round z to two decimals.

μX = 12, σX = 1.5μY = 20, σY = 2X + Y > 30 min
P =
4.Medium
78.25103.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 78.25 and 103.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 78.25x2 = 103.75
P =
5.Hard
557085100115130145pointsbottom 75%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded bottom 75% is to the left of it. Find the cut-off x.

μ = 100 pointsσ = 15 points75%
x = points
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. z = 1.66
  2. 2. P(X < x) = 0.5987
  3. 3. P = 0.7881
  4. 4. P = 0.5252
  5. 5. x = 110.1 points
  6. 6. P = 0.7389

Full step-by-step solutions: practise this topic on examproblems.com.