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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1.Easy
−3−2−10123zshaded area to the left of z = 0.9625

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9625. Find z to two decimals.

A = 0.9625
z =
2.Easy
μ = 3227.5P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 27.5 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 27.5
P(X > x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.0250

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0250. Find z to two decimals.

A = 0.0250
z =
4.Medium
22.443.1P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 22.4 and 43.1 min? Give P as a decimal.

μ = 32σ = 6x1 = 22.4x2 = 43.1
P =
5.Hard
μ = 32x = ?97.5%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 32σ = 6P = 97.5%
x = min
6.Hard
0.05 mm0D − d?

Hole diameters D are normal with mean 25.05 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.02 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 = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. z = 1.78
  2. 2. P(X > x) = 0.7734
  3. 3. z = 1.96
  4. 4. P = 0.913
  5. 5. x = 43.76 min
  6. 6. P = 0.9875

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