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
40 mmσ = ?X − Y

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of the difference X − Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
2.Easy
−3−2−10123zshaded area to the left of z = 0.2810

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2810. Find z to two decimals.

A = 0.2810
z =
3.Medium
480 g477.9 gT = X₁ + … + X₁₂?

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 12 of them is below 477.9 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 12< 477.9 g
P =
4.Medium
510 kg539.4 kgT = X₁ + … + X₆?

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 6 of them is below 539.4 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 6< 539.4 kg
P =
5.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 =
6.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.03 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.015 mm
P =

Answer key

  1. 1. σ = 0.5 mm
  2. 2. z = −0.58
  3. 3. P = 0.305
  4. 4. P = 0.8413
  5. 5. P = 0.7881
  6. 6. P = 0.9207

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