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 = 500548P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is below 548 h? Find P(X < x) as a decimal.

μ = 500σ = 40x = 548
P(X < x) =
2.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) =
3.Medium
−3−2−10123zshaded area to the right of z = 0.9545

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9545. Find z to two decimals.

A = 0.9545
z =
4.Medium
32 min30 minX + Y?

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 30 min. Round z to two decimals.

μX = 12, σX = 1.5μY = 20, σY = 2X + Y > 30 min
P =
5.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.01 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.03 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.01 mm
P =
6.Hard
557085100115130145pointstop 90%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 90% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points90%
x = points

Answer key

  1. 1. P(X < x) = 0.8849
  2. 2. P(X > x) = 0.8413
  3. 3. z = −1.69
  4. 4. P = 0.7881
  5. 5. P = 0.983
  6. 6. x = 80.8 points

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