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 = 0.3156

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3156. Find z to two decimals.

A = 0.3156
z =
2.Easy
750 gσ = ?X + Y

X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
3.Medium
−3−2−10123zshaded area to the right of z = 0.8238

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8238. Find z to two decimals.

A = 0.8238
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9031

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9031. Find z to two decimals.

A = 0.9031
z =
5.Hard
10 g0X − Y?

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 500 g, σX = 8 gμY = 490 g, σY = 6 g
P =
6.Hard
μ = 32x = ?20%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 20% of them lie (the 20th percentile).

μ = 32σ = 6P = 20%
x = min

Answer key

  1. 1. z = −0.48
  2. 2. σ = 9.849 g
  3. 3. z = −0.93
  4. 4. z = 1.66
  5. 5. P = 0.8413
  6. 6. x = 26.95 min

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