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 = 0.9582

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9582. Find z to two decimals.

A = 0.9582
z =
2.Easy
μ = 250252P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 252 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 252
P(X < x) =
3.Medium
−3−2−10123zshaded area between −z and z = 0.3616

Drag z so that the shaded area between −z and z under the standard normal curve is 0.3616. Find z to two decimals.

A = 0.3616
z =
4.Medium
93.25112P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 93.25 and 112 points? Give P as a decimal.

μ = 100σ = 15x1 = 93.25x2 = 112
P =
5.Hard
μ = 500x = ?25%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 25% of them lie (the 25th percentile).

μ = 500σ = 40P = 25%
x = h
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 = 1.73
  2. 2. P(X < x) = 0.6554
  3. 3. z = 0.47
  4. 4. P = 0.4618
  5. 5. x = 473 h
  6. 6. P = 0.9875

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