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 = 178189.55P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 189.55 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 189.55
P(X > x) =
2.Easy
−250 gσ = ?X − Y

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
3.Medium
680 kg713.9 kgT = X₁ + … + X₈?

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 8 of them exceeds 713.9 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 8> 713.9 kg
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.9890

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9890. Find z to two decimals.

A = 0.9890
z =
5.Hard
μ = 250x = ?95%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 95% of them lie (the 95th percentile).

μ = 250σ = 5P = 95%
x = g
6.Hard
μ = 178x = ?80%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 80% of them lie (the 80th percentile).

μ = 178σ = 7P = 80%
x = cm

Answer key

  1. 1. P(X > x) = 0.04947
  2. 2. σ = 9.849 g
  3. 3. P = 0.1587
  4. 4. z = −2.29
  5. 5. x = 258.2 g
  6. 6. x = 183.9 cm

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