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
−8 minσ = ?X − Y

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
2.Easy
μ = 10092.5P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 92.5 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 92.5
P(X < x) =
3.Medium
167.5188.85P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 167.5 and 188.85 cm? Give P as a decimal.

μ = 178σ = 7x1 = 167.5x2 = 188.85
P =
4.Medium
−3−2−10123zshaded area between −z and z = 0.9634

Drag z so that the shaded area between −z and z under the standard normal curve is 0.9634. Find z to two decimals.

A = 0.9634
z =
5.Hard
235240245250255260265gbottom 20%

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded bottom 20% is to the left of it. Find the cut-off x.

μ = 250 gσ = 5 g20%
x = g
6.Hard
μ = 32x = ?99%

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 99% of them lie (the 99th percentile).

μ = 32σ = 6P = 99%
x = min

Answer key

  1. 1. σ = 2.5 min
  2. 2. P(X < x) = 0.3085
  3. 3. P = 0.8726
  4. 4. z = 2.09
  5. 5. x = 245.8 g
  6. 6. x = 45.96 min

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