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 = 500574P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is below 574 h? Find P(X < x) as a decimal.

μ = 500σ = 40x = 574
P(X < x) =
2.Easy
−250 gσ = ?X − Y

X is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μX = 250 g, σX = 4 gμY = 500 g, σY = 9 g
σ = g
3.Medium
480542P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 480 and 542 h? Give P as a decimal.

μ = 500σ = 40x1 = 480x2 = 542
P =
4.Medium
76.75103.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 76.75 and 103.75 points? Give P as a decimal.

μ = 100σ = 15x1 = 76.75x2 = 103.75
P =
5.Hard
μ = 100x = ?99%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 100σ = 15P = 99%
x = points
6.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

Answer key

  1. 1. P(X < x) = 0.9678
  2. 2. σ = 9.849 g
  3. 3. P = 0.5446
  4. 4. P = 0.5381
  5. 5. x = 134.9 points
  6. 6. x = 533.7 h

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