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 = 0.0951

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0951. Find z to two decimals.

A = 0.0951
z =
2.Easy
32 minσ = ?X + Y

X and Y are independent normal variables for the time for two consecutive process steps: X has mean 12 min and standard deviation 1.5 min, Y has mean 20 min and standard deviation 2 min. Find the standard deviation σ of X + Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
−3−2−10123zshaded area between −z and z = 0.7887

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7887. Find z to two decimals.

A = 0.7887
z =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9715

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9715. Find z to two decimals.

A = 0.9715
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 = 178x = ?80%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 80% of them lie (the 80th percentile).

μ = 178σ = 7P = 80%
x = cm

Answer key

  1. 1. z = −1.31
  2. 2. σ = 2.5 min
  3. 3. z = 1.25
  4. 4. z = 2.19
  5. 5. P = 0.8413
  6. 6. x = 183.9 cm

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