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 = 500562P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 562 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 562
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.7190

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7190. Find z to two decimals.

A = 0.7190
z =
3.Medium
32 min34.5 minX + Y?

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 34.5 min. Round z to two decimals.

μX = 12, σX = 1.5μY = 20, σY = 2X + Y > 34.5 min
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.5467

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5467. Find z to two decimals.

A = 0.5467
z =
5.Hard
μ = 178x = ?5%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 5% of them lie (the 5th percentile).

μ = 178σ = 7P = 5%
x = cm
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. P(X > x) = 0.06057
  2. 2. z = 0.58
  3. 3. P = 0.1587
  4. 4. z = 0.75
  5. 5. x = 166.5 cm
  6. 6. P = 0.8133

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