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 = 0.9744

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9744. Find z to two decimals.

A = 0.9744
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.3015

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.3015. Find z to two decimals.

A = 0.3015
z =
3.Medium
−3−2−10123zshaded area to the right of z = 0.0708

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0708. Find z to two decimals.

A = 0.0708
z =
4.Medium
300 kg300.9 kgT = X₁ + … + X₁₂?

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 12 of them exceeds 300.9 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 12> 300.9 kg
P =
5.Hard
μ = 250x = ?5%

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

μ = 250σ = 5P = 5%
x = g
6.Hard
μ = 32x = ?5%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 5% of them lie (the 5th percentile).

μ = 32σ = 6P = 5%
x = min

Answer key

  1. 1. z = 1.95
  2. 2. z = −0.52
  3. 3. z = 1.47
  4. 4. P = 0.3015
  5. 5. x = 241.8 g
  6. 6. x = 22.13 min

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