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 = 0.0465

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0465. Find z to two decimals.

A = 0.0465
z =
2.Easy
200 mmσ = ?X + Y

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μX = 120 mm, σX = 0.3 mmμY = 80 mm, σY = 0.4 mm
σ = mm
3.Medium
225 kg225.8 kgT = X₁ + … + X₉?

The masses of bags of cement are independent and normal with mean 25 kg and standard deviation 0.5 kg. Find the probability P that the total mass of 9 of them exceeds 225.8 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 9> 225.8 kg
P =
4.Medium
82112P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 82 and 112 points? Give P as a decimal.

μ = 100σ = 15x1 = 82x2 = 112
P =
5.Hard
380420460500540580620hbottom 95%

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

μ = 500 hσ = 40 h95%
x = h
6.Hard
10 cm0X − Y?

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 180 cm, σX = 10 cmμY = 170 cm, σY = 12 cm
P =

Answer key

  1. 1. z = −1.68
  2. 2. σ = 0.5 mm
  3. 3. P = 0.2981
  4. 4. P = 0.6731
  5. 5. x = 566 h
  6. 6. P = 0.7389

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