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
μ = 178169.6P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is below 169.6 cm? Find P(X < x) as a decimal.

μ = 178σ = 7x = 169.6
P(X < x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.8340

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8340. Find z to two decimals.

A = 0.8340
z =
3.Medium
4567.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 45 and 67.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 45x2 = 67.5
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0475

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0475. Find z to two decimals.

A = 0.0475
z =
5.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
6.Hard
380420460500540580620hbottom 70%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded bottom 70% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h70%
x = h

Answer key

  1. 1. P(X < x) = 0.1151
  2. 2. z = 0.97
  3. 3. P = 0.576
  4. 4. z = 1.67
  5. 5. x = 527 h
  6. 6. x = 521 h

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