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 = 100112.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 112.75 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 112.75
P(X > x) =
2.Easy
32 minσ = ?X + Y

X and Y are independent normal variables for the time for two consecutive process steps: X has mean 12 min and standard deviation 1.5 min, Y has mean 20 min and standard deviation 2 min. Find the standard deviation σ of X + Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
105 s98.6 sX + Y?

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 98.6 s. Round z to two decimals.

μX = 60, σX = 5μY = 45, σY = 4X + Y > 98.6 s
P =
4.Medium
166.8186.75P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 166.8 and 186.75 cm? Give P as a decimal.

μ = 178σ = 7x1 = 166.8x2 = 186.75
P =
5.Hard
380420460500540580620hbottom 80%

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded bottom 80% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h80%
x = h
6.Hard
557085100115130145pointstop 75%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 75% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points75%
x = points

Answer key

  1. 1. P(X > x) = 0.1977
  2. 2. σ = 2.5 min
  3. 3. P = 0.8413
  4. 4. P = 0.8396
  5. 5. x = 534 h
  6. 6. x = 90 points

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