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 = 0.8365

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8365. Find z to two decimals.

A = 0.8365
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9265

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9265. Find z to two decimals.

A = 0.9265
z =
3.Medium
105 s95.4 sX + Y?

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 95.4 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 95.4 s
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9749

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9749. Find z to two decimals.

A = 0.9749
z =
5.Hard
157164171178185192199cmtop 70%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 70% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm70%
x = cm
6.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.02 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 = 0.02 mmshaft: μ = 25 mm, σ = 0.02 mm
P =

Answer key

  1. 1. z = 0.98
  2. 2. z = 1.45
  3. 3. P = 0.9332
  4. 4. z = 2.24
  5. 5. x = 174.4 cm
  6. 6. P = 0.8554

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