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 = 0.0150

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0150. Find z to two decimals.

A = 0.0150
z =
2.Easy
−250 gσ = ?X − Y

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
3.Medium
−3−2−10123zshaded area to the right of z = 0.1446

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.1446. Find z to two decimals.

A = 0.1446
z =
4.Medium
100123.25P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 100 and 123.25 points? Give P as a decimal.

μ = 100σ = 15x1 = 100x2 = 123.25
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 = 100x = ?10%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 10% of them lie (the 10th percentile).

μ = 100σ = 15P = 10%
x = points

Answer key

  1. 1. z = −2.17
  2. 2. σ = 9.849 g
  3. 3. z = 1.06
  4. 4. P = 0.4394
  5. 5. P = 0.7881
  6. 6. x = 80.78 points

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