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 = 0.9793

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9793. Find z to two decimals.

A = 0.9793
z =
2.Easy
−3−2−10123zshaded area to the left of z = 0.1736

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1736. Find z to two decimals.

A = 0.1736
z =
3.Medium
425 kg398.2 kgT = X₁ + … + X₅?

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 5 of them exceeds 398.2 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 5> 398.2 kg
P =
4.Medium
200 mm200.8 mmX + Y?

X is normal with mean 120 mm and standard deviation 0.3 mm; Y is independent and normal with mean 80 mm and standard deviation 0.4 mm. Find the probability P that X + Y is more than 200.8 mm. Round z to two decimals.

μX = 120, σX = 0.3μY = 80, σY = 0.4X + Y > 200.8 mm
P =
5.Hard
557085100115130145pointsbottom 25%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded bottom 25% is to the left of it. Find the cut-off x.

μ = 100 pointsσ = 15 points25%
x = points
6.Hard
157164171178185192199cmtop 25%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 25% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm25%
x = cm

Answer key

  1. 1. z = 2.04
  2. 2. z = −0.94
  3. 3. P = 0.8413
  4. 4. P = 0.0548
  5. 5. x = 90 points
  6. 6. x = 182.7 cm

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