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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Name: ____________________   Date: ____________

1.Easy
μ = 100106.75P = ?

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 106.75 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 106.75
P(X < x) =
2.Easy
−8 minσ = ?X − Y

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the standard deviation σ of the difference X − Y.

μX = 12 min, σX = 1.5 minμY = 20 min, σY = 2 min
σ = min
3.Medium
425 kg384.8 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 384.8 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 5> 384.8 kg
P =
4.Medium
−3−2−10123zshaded area to the right of z = 0.9582

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9582. Find z to two decimals.

A = 0.9582
z =
5.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.03 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.015 mm
P =
6.Hard
10 cm0X − Y?

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 180 cm, σX = 10 cmμY = 170 cm, σY = 12 cm
P =

Answer key

  1. 1. P(X < x) = 0.6736
  2. 2. σ = 2.5 min
  3. 3. P = 0.9332
  4. 4. z = −1.73
  5. 5. P = 0.9515
  6. 6. P = 0.7389

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