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 = 10094P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 94 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 94
P(X > x) =
2.Easy
−8 minσ = ?X − 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 standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
105 s114.6 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 114.6 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 114.6 s
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9342

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9342. Find z to two decimals.

A = 0.9342
z =
5.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 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 = 25.03 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.01 mm
P =
6.Hard
μ = 500x = ?95%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 95% of them lie (the 95th percentile).

μ = 500σ = 40P = 95%
x = h

Answer key

  1. 1. P(X > x) = 0.6554
  2. 2. σ = 2.5 min
  3. 3. P = 0.06681
  4. 4. z = 1.84
  5. 5. P = 0.9515
  6. 6. x = 565.8 h

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