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 = 10094P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 94 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 94
P(X < x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.1423

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1423. Find z to two decimals.

A = 0.1423
z =
3.Medium
502532P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 502 and 532 h? Give P as a decimal.

μ = 500σ = 40x1 = 502x2 = 532
P =
4.Medium
245256.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 245 and 256.25 g? Give P as a decimal.

μ = 250σ = 5x1 = 245x2 = 256.25
P =
5.Hard
μ = 500x = ?80%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 80% of them lie (the 80th percentile).

μ = 500σ = 40P = 80%
x = h
6.Hard
μ = 178x = ?75%

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 75% of them lie (the 75th percentile).

μ = 178σ = 7P = 75%
x = cm

Answer key

  1. 1. P(X < x) = 0.3446
  2. 2. z = −1.07
  3. 3. P = 0.2682
  4. 4. P = 0.7357
  5. 5. x = 533.7 h
  6. 6. x = 182.7 cm

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