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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0250. Find z to two decimals.

A = 0.0250

z =

3.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 =

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 16 of them is below 1288 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 16< 1288 kg

P =

5.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 97.5% of them lie (the 97.5th percentile).

μ = 100σ = 15P = 97.5%

x = points

6.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded top 20% is to the right of it. Find the cut-off x.

μ = 500 hσ = 40 h20%

x = h

Answer key

1. σ = 2.5 min
2. z = −1.96
3. P = 0.02275
4. P = 0.06681
5. x = 129.4 points
6. x = 534 h

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