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
μ = 250254P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 254 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 254
P(X < x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.7794

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7794. Find z to two decimals.

A = 0.7794
z =
3.Medium
−3−2−10123zshaded area between −z and z = 0.5346

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5346. Find z to two decimals.

A = 0.5346
z =
4.Medium
502540P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 502 and 540 h? Give P as a decimal.

μ = 500σ = 40x1 = 502x2 = 540
P =
5.Hard
μ = 32x = ?20%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 20% of them lie (the 20th percentile).

μ = 32σ = 6P = 20%
x = min
6.Hard
μ = 32x = ?10%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 10% of them lie (the 10th percentile).

μ = 32σ = 6P = 10%
x = min

Answer key

  1. 1. P(X < x) = 0.7881
  2. 2. z = 0.77
  3. 3. z = 0.73
  4. 4. P = 0.3214
  5. 5. x = 26.95 min
  6. 6. x = 24.31 min

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