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 battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is below 534 h? Find P(X < x) as a decimal.

μ = 500σ = 40x = 534

P(X < x) =

3.Medium

Drag z so that the shaded area between −z and z under the standard normal curve is 0.8557. Find z to two decimals.

A = 0.8557

z =

4.Medium

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 9 of them is below 837 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 9< 837 kg

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 90% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h90%

x = h

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 60% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points60%

x = points

Answer key

1. σ = 2.5 min
2. P(X < x) = 0.8023
3. z = 1.46
4. P = 0.9772
5. x = 449 h
6. x = 62.5 points

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