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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9463. Find z to two decimals.

A = 0.9463

z =

2.Easy

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.

μ_X = 12 min, σ_X = 1.5 minμ_Y = 20 min, σ_Y = 2 min

σ = min

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.0228. Find z to two decimals.

A = 0.0228

z =

4.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 20.3 and 33.5 min? Give P as a decimal.

μ = 32σ = 6x₁ = 20.3x₂ = 33.5

P =

5.Hard

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.

μ_X = 52 s, σ_X = 4 sμ_Y = 48 s, σ_Y = 3 s

P =

6.Hard

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.01 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.02 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.02 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm

P =

Answer key

1. z = 1.61
2. σ = 2.5 min
3. z = 2
4. P = 0.5731
5. P = 0.7881
6. P = 0.8133

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