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 = 3223.3P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is above 23.3 min? Find P(X > x) as a decimal.

μ = 32σ = 6x = 23.3
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9633

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9633. Find z to two decimals.

A = 0.9633
z =
3.Medium
400 kg397 kgT = X₁ + … + X₁₆?

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 16 of them is below 397 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 16< 397 kg
P =
4.Medium
100107.5P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 100 and 107.5 points? Give P as a decimal.

μ = 100σ = 15x1 = 100x2 = 107.5
P =
5.Hard
μ = 100x = ?20%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 20% of them lie (the 20th percentile).

μ = 100σ = 15P = 20%
x = points
6.Hard
235240245250255260265gtop 75%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 75% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g75%
x = g

Answer key

  1. 1. P(X > x) = 0.9265
  2. 2. z = 1.79
  3. 3. P = 0.06681
  4. 4. P = 0.1915
  5. 5. x = 87.38 points
  6. 6. x = 246.7 g

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