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 = 0.1292

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1292. Find z to two decimals.

A = 0.1292
z =
2.Easy
μ = 250246.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 246.25 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 246.25
P(X < x) =
3.Medium
240.25260.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 240.25 and 260.25 g? Give P as a decimal.

μ = 250σ = 5x1 = 240.25x2 = 260.25
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.8212

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8212. Find z to two decimals.

A = 0.8212
z =
5.Hard
4 s0X − Y?

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 52 s, σX = 4 sμY = 48 s, σY = 3 s
P =
6.Hard
μ = 178x = ?20%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 20% of them lie (the 20th percentile).

μ = 178σ = 7P = 20%
x = cm

Answer key

  1. 1. z = −1.13
  2. 2. P(X < x) = 0.2266
  3. 3. P = 0.9542
  4. 4. z = −0.92
  5. 5. P = 0.7881
  6. 6. x = 172.1 cm

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