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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Name: ____________________   Date: ____________

1.Easy
μ = 3225.1P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 25.1 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 25.1
P(X > x) =
2.Easy
μ = 100112.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 112.75 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 112.75
P(X < x) =
3.Medium
85130.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 85 and 130.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 85x2 = 130.75
P =
4.Medium
640 g635.2 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 635.2 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 16> 635.2 g
P =
5.Hard
0.02 mm0D − d?

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.015 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 = 25.02 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.01 mm
P =
6.Hard
35455565758595pointstop 70%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 70% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points70%
x = points

Answer key

  1. 1. P(X > x) = 0.8749
  2. 2. P(X < x) = 0.8023
  3. 3. P = 0.8212
  4. 4. P = 0.8413
  5. 5. P = 0.8665
  6. 6. x = 59.8 points

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