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
−250 gσ = ?X − Y

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
2.Easy
μ = 10088P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 88 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 88
P(X > x) =
3.Medium
45.577P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 45.5 and 77 points? Give P as a decimal.

μ = 65σ = 10x1 = 45.5x2 = 77
P =
4.Medium
100 kg102 kgT = X₁ + … + X₄?

The masses of bags of cement are independent and normal with mean 25 kg and standard deviation 0.5 kg. Find the probability P that the total mass of 4 of them exceeds 102 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 4> 102 kg
P =
5.Hard
μ = 178x = ?90%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 90% of them lie (the 90th percentile).

μ = 178σ = 7P = 90%
x = cm
6.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.01 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 = 0.01 mmshaft: μ = 25 mm, σ = 0.015 mm
P =

Answer key

  1. 1. σ = 9.849 g
  2. 2. P(X > x) = 0.7881
  3. 3. P = 0.8593
  4. 4. P = 0.02275
  5. 5. x = 187 cm
  6. 6. P = 0.8665

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