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
μ = 10085P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 85 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 85
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.3483

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3483. Find z to two decimals.

A = 0.3483
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.9463

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9463. Find z to two decimals.

A = 0.9463
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.5223

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5223. Find z to two decimals.

A = 0.5223
z =
5.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 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 = 25.02 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.Hard
μ = 500x = ?20%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 20% of them lie (the 20th percentile).

μ = 500σ = 40P = 20%
x = h

Answer key

  1. 1. P(X > x) = 0.8413
  2. 2. z = −0.39
  3. 3. z = −1.61
  4. 4. z = 0.71
  5. 5. P = 0.8264
  6. 6. x = 466.3 h

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