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
−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
2.Easy
−3−2−10123zshaded area to the left of z = 0.7123

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7123. Find z to two decimals.

A = 0.7123
z =
3.Medium
171192.35P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 171 and 192.35 cm? Give P as a decimal.

μ = 178σ = 7x1 = 171x2 = 192.35
P =
4.Medium
750 g757.9 gX + Y?

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the probability P that X + Y is more than 757.9 g. Round z to two decimals.

μX = 250, σX = 4μY = 500, σY = 9X + Y > 757.9 g
P =
5.Hard
μ = 250x = ?95%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 95% of them lie (the 95th percentile).

μ = 250σ = 5P = 95%
x = g
6.Hard
μ = 65x = ?20%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 20% of them lie (the 20th percentile).

μ = 65σ = 10P = 20%
x = points

Answer key

  1. 1. σ = 2.5 min
  2. 2. z = 0.56
  3. 3. P = 0.8212
  4. 4. P = 0.2119
  5. 5. x = 258.2 g
  6. 6. x = 56.58 points

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