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 = 0.0409

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0409. Find z to two decimals.

A = 0.0409
z =
2.Easy
μ = 3234.4P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 34.4 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 34.4
P(X < x) =
3.Medium
488574P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 488 and 574 h? Give P as a decimal.

μ = 500σ = 40x1 = 488x2 = 574
P =
4.Medium
105 s111.4 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 111.4 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 111.4 s
P =
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
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 = −1.74
  2. 2. P(X < x) = 0.6554
  3. 3. P = 0.5858
  4. 4. P = 0.1587
  5. 5. x = 533.7 h
  6. 6. x = 26.95 min

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