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
−3−2−10123zshaded area to the left of z = 0.0351

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0351. Find z to two decimals.

A = 0.0351
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.1635

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1635. Find z to two decimals.

A = 0.1635
z =
3.Medium
−3−2−10123zshaded area between −z and z = 0.7775

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7775. Find z to two decimals.

A = 0.7775
z =
4.Medium
200 mm199.5 mmX + Y?

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the probability P that X + Y is more than 199.5 mm. Round z to two decimals.

μX = 120, σX = 0.3μY = 80, σY = 0.4X + Y > 199.5 mm
P =
5.Hard
0.05 mm0D − d?

Hole diameters D are normal with mean 25.05 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 = 25.05 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm
P =
6.Hard
557085100115130145pointstop 5%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 5% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points5%
x = points

Answer key

  1. 1. z = −1.81
  2. 2. z = −0.98
  3. 3. z = 1.22
  4. 4. P = 0.8413
  5. 5. P = 0.9875
  6. 6. x = 124.6 points

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