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

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

2.Easy

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 29.6 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 29.6

P(X < x) =

3.Medium

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction lies between 502 and 574 h? Give P as a decimal.

μ = 500σ = 40x₁ = 502x₂ = 574

P =

4.Medium

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 29.3 and 37.1 min? Give P as a decimal.

μ = 32σ = 6x₁ = 29.3x₂ = 37.1

P =

5.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 80% of them lie (the 80th percentile).

μ = 250σ = 5P = 80%

x = g

6.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 =

Answer key

1. σ = 2.5 min
2. P(X < x) = 0.3446
3. P = 0.4479
4. P = 0.476
5. x = 254.2 g
6. P = 0.7881

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