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
40 mmσ = ?X − Y

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of the difference X − Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
2.Easy
μ = 10073.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 73.75 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 73.75
P(X > x) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.1379

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.1379. Find z to two decimals.

A = 0.1379
z =
4.Medium
640 g649.6 gT = X₁ + … + X₁₆?

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 16 of them exceeds 649.6 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 16> 649.6 g
P =
5.Hard
μ = 65x = ?97.5%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 65σ = 10P = 97.5%
x = points
6.Hard
μ = 32x = ?5%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 5% of them lie (the 5th percentile).

μ = 32σ = 6P = 5%
x = min

Answer key

  1. 1. σ = 0.5 mm
  2. 2. P(X > x) = 0.9599
  3. 3. z = 1.09
  4. 4. P = 0.02275
  5. 5. x = 84.6 points
  6. 6. x = 22.13 min

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