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 = 3225.1P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 25.1 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 25.1
P(X < x) =
2.Easy
μ = 500520P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 520 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 520
P(X > x) =
3.Medium
−3−2−10123zshaded area between −z and z = 0.5587

Drag z so that the shaded area between −z and z under the standard normal curve is 0.5587. Find z to two decimals.

A = 0.5587
z =
4.Medium
169.95181.85P = ?

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 169.95 and 181.85 cm? Give P as a decimal.

μ = 178σ = 7x1 = 169.95x2 = 181.85
P =
5.Hard
0.03 mm0D − d?

Hole diameters D are normal with mean 25.03 mm and standard deviation 0.02 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.01 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 = 0.02 mmshaft: μ = 25 mm, σ = 0.01 mm
P =
6.Hard
4 s0X − Y?

Runner A's lap time X and runner B's lap time Y are independent and normal: X has mean 52 s and standard deviation 4 s, Y has mean 48 s and standard deviation 3 s. Find the probability P that X is greater than Y. Round z to two decimals.

μX = 52 s, σX = 4 sμY = 48 s, σY = 3 s
P =

Answer key

  1. 1. P(X < x) = 0.1251
  2. 2. P(X > x) = 0.3085
  3. 3. z = 0.77
  4. 4. P = 0.5838
  5. 5. P = 0.9099
  6. 6. P = 0.7881

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