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

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction is below 38.3 min? Find P(X < x) as a decimal.

μ = 32σ = 6x = 38.3

P(X < x) =

2.Easy

X and Y are independent normal variables for the length of part A plus part B in an assembly: X has mean 120 mm and standard deviation 0.3 mm, Y has mean 80 mm and standard deviation 0.4 mm. Find the standard deviation σ of X + Y.

μ_X = 120 mm, σ_X = 0.3 mmμ_Y = 80 mm, σ_Y = 0.4 mm

σ = mm

3.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 70.75 and 108.25 points? Give P as a decimal.

μ = 100σ = 15x₁ = 70.75x₂ = 108.25

P =

4.Medium

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 probability P that X + Y is more than 37 min. Round z to two decimals.

μ_X = 12, σ_X = 1.5μ_Y = 20, σ_Y = 2X + Y > 37 min

P =

5.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 75% of them lie (the 75th percentile).

μ = 65σ = 10P = 75%

x = points

6.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 5% of them lie (the 5th percentile).

μ = 500σ = 40P = 5%

x = h

Answer key

1. P(X < x) = 0.8531
2. σ = 0.5 mm
3. P = 0.6833
4. P = 0.02275
5. x = 71.75 points
6. x = 434.2 h

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