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 = 0.1539

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1539. Find z to two decimals.

A = 0.1539
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.0465

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0465. Find z to two decimals.

A = 0.0465
z =
3.Medium
95.5112.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 95.5 and 112.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 95.5x2 = 112.75
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.8764

Drag z so that the shaded area between −z and z under the standard normal curve is 0.8764. Find z to two decimals.

A = 0.8764
z =
5.Hard
μ = 500x = ?99%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 99% of them lie (the 99th percentile).

μ = 500σ = 40P = 99%
x = h
6.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 0.02 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 = 0.02 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. z = −1.02
  2. 2. z = −1.68
  3. 3. P = 0.4202
  4. 4. z = 1.54
  5. 5. x = 593.1 h
  6. 6. P = 0.9616

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