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 = 178192.35P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 192.35 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 192.35
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.8159

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8159. Find z to two decimals.

A = 0.8159
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.8554

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.8554. Find z to two decimals.

A = 0.8554
z =
4.Medium
53.575.5P = ?

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 53.5 and 75.5 points? Give P as a decimal.

μ = 65σ = 10x1 = 53.5x2 = 75.5
P =
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 = ?25%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 25% of them lie (the 25th percentile).

μ = 178σ = 7P = 25%
x = cm

Answer key

  1. 1. P(X > x) = 0.02018
  2. 2. z = 0.9
  3. 3. z = −1.06
  4. 4. P = 0.7281
  5. 5. P = 0.7881
  6. 6. x = 173.3 cm

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