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 = 100118P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 118 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 118
P(X > x) =
2.Easy
μ = 178175.2P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 175.2 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 175.2
P(X < x) =
3.Medium
750 g754.9 gX + 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 probability P that X + Y is more than 754.9 g. Round z to two decimals.

μX = 250, σX = 4μY = 500, σY = 9X + Y > 754.9 g
P =
4.Medium
488574P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 488 and 574 h? Give P as a decimal.

μ = 500σ = 40x1 = 488x2 = 574
P =
5.Hard
μ = 32x = ?25%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 25% of them lie (the 25th percentile).

μ = 32σ = 6P = 25%
x = min
6.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 0.02 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.03 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. P(X > x) = 0.1151
  2. 2. P(X < x) = 0.3446
  3. 3. P = 0.3085
  4. 4. P = 0.5858
  5. 5. x = 27.95 min
  6. 6. P = 0.9099

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