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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Name: ____________________   Date: ____________

1.Easy
−3−2−10123zshaded area to the left of z = 0.9890

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9890. Find z to two decimals.

A = 0.9890
z =
2.Easy
μ = 6580.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is below 80.5 points? Find P(X < x) as a decimal.

μ = 65σ = 10x = 80.5
P(X < x) =
3.Medium
400 g405.7 gT = X₁ + … + X₁₀?

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 10 of them is below 405.7 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 10< 405.7 g
P =
4.Medium
82.75112.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 82.75 and 112.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 82.75x2 = 112.75
P =
5.Hard
380420460500540580620htop 95%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 95% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h95%
x = h
6.Hard
μ = 500x = ?75%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 75% of them lie (the 75th percentile).

μ = 500σ = 40P = 75%
x = h

Answer key

  1. 1. z = 2.29
  2. 2. P(X < x) = 0.9394
  3. 3. P = 0.9332
  4. 4. P = 0.6773
  5. 5. x = 434 h
  6. 6. x = 527 h

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