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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Name: ____________________   Date: ____________

1.Easy
−3−2−10123zshaded area to the left of z = 0.2514

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.2514. Find z to two decimals.

A = 0.2514
z =
2.Easy
μ = 6560.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is above 60.5 points? Find P(X > x) as a decimal.

μ = 65σ = 10x = 60.5
P(X > x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.0188

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0188. Find z to two decimals.

A = 0.0188
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9660

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9660. Find z to two decimals.

A = 0.9660
z =
5.Hard
0.05 mm0D − d?

Hole diameters D are normal with mean 25.05 mm and standard deviation 0.02 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 = 25.05 mm, σ = 0.02 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.01 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 = 0.01 mmshaft: μ = 25 mm, σ = 0.015 mm
P =

Answer key

  1. 1. z = −0.67
  2. 2. P(X > x) = 0.6736
  3. 3. z = 2.08
  4. 4. z = 2.12
  5. 5. P = 0.9772
  6. 6. P = 0.9515

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