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 = 0.0968

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0968. Find z to two decimals.

A = 0.0968
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.3372

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3372. Find z to two decimals.

A = 0.3372
z =
3.Medium
360 g363.6 gT = X₁ + … + X₉?

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 9 of them is below 363.6 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 9< 363.6 g
P =
4.Medium
245.25255P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 245.25 and 255 g? Give P as a decimal.

μ = 250σ = 5x1 = 245.25x2 = 255
P =
5.Hard
μ = 250x = ?80%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 80% of them lie (the 80th percentile).

μ = 250σ = 5P = 80%
x = g
6.Hard
μ = 65x = ?95%

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 95% of them lie (the 95th percentile).

μ = 65σ = 10P = 95%
x = points

Answer key

  1. 1. z = −1.3
  2. 2. z = −0.42
  3. 3. P = 0.8413
  4. 4. P = 0.6703
  5. 5. x = 254.2 g
  6. 6. x = 81.45 points

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