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 = 0.3015

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3015. Find z to two decimals.

A = 0.3015
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.3085

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3085. Find z to two decimals.

A = 0.3085
z =
3.Medium
200 mm199.8 mmX + Y?

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the probability P that X + Y is more than 199.8 mm. Round z to two decimals.

μX = 120, σX = 0.3μY = 80, σY = 0.4X + Y > 199.8 mm
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.7923

Drag z so that the shaded area between −z and z under the standard normal curve is 0.7923. Find z to two decimals.

A = 0.7923
z =
5.Hard
μ = 500x = ?80%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 80% of them lie (the 80th percentile).

μ = 500σ = 40P = 80%
x = h
6.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 =

Answer key

  1. 1. z = −0.52
  2. 2. z = −0.5
  3. 3. P = 0.6554
  4. 4. z = 1.26
  5. 5. x = 533.7 h
  6. 6. P = 0.8413

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