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
−3−2−10123zshaded area to the left of z = 0.1841

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1841. Find z to two decimals.

A = 0.1841
z =
2.Easy
μ = 3239.5P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 39.5 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 39.5
P(X > x) =
3.Medium
95.5118.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 95.5 and 118.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 95.5x2 = 118.75
P =
4.Medium
192 kg195.2 kgT = X₁ + … + X₁₆?

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 16 of them exceeds 195.2 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 16> 195.2 kg
P =
5.Hard
0.04 mm0D − d?

Hole diameters D are normal with mean 25.04 mm and standard deviation 0.02 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 = 25.04 mm, σ = 0.02 mmshaft: μ = 25 mm, σ = 0.01 mm
P =
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 0.02 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.02 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. z = −0.9
  2. 2. P(X > x) = 0.1056
  3. 3. P = 0.5123
  4. 4. P = 0.1587
  5. 5. P = 0.9633
  6. 6. P = 0.8133

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