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 bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is above 260 g? Find P(X > x) as a decimal.

μ = 250σ = 5x = 260

P(X > x) =

3.Medium

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 8 of them is below 316.6 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 8< 316.6 g

P =

4.Medium

The masses of bags of cement are independent and normal with mean 25 kg and standard deviation 0.5 kg. Find the probability P that the total mass of 9 of them exceeds 225.8 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 9> 225.8 kg

P =

5.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Drag the cut-off so the shaded top 40% is to the right of it. Find the cut-off x.

μ = 178 cmσ = 7 cm40%

x = cm

6.Hard

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 10% of them lie (the 10th percentile).

μ = 32σ = 6P = 10%

x = min

Answer key

1. σ = 2.5 min
2. P(X > x) = 0.02275
3. P = 0.1587
4. P = 0.2981
5. x = 179.8 cm
6. x = 24.31 min

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