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 = 0.8849

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8849. Find z to two decimals.

A = 0.8849
z =
2.Easy
μ = 100115P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 115 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 115
P(X > x) =
3.Medium
510 kg524.7 kgT = X₁ + … + X₆?

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 6 of them is below 524.7 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 6< 524.7 kg
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.0228

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0228. Find z to two decimals.

A = 0.0228
z =
5.Hard
μ = 178x = ?25%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 25% of them lie (the 25th percentile).

μ = 178σ = 7P = 25%
x = cm
6.Hard
μ = 500x = ?5%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 5% of them lie (the 5th percentile).

μ = 500σ = 40P = 5%
x = h

Answer key

  1. 1. z = 1.2
  2. 2. P(X > x) = 0.1587
  3. 3. P = 0.6915
  4. 4. z = 2
  5. 5. x = 173.3 cm
  6. 6. x = 434.2 h

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