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 is normal with mean 250 g and standard deviation 4 g; Y is independent and normal with mean 500 g and standard deviation 9 g. Find the standard deviation σ of the difference X − Y.

μ_X = 250 g, σ_X = 4 gμ_Y = 500 g, σ_Y = 9 g

σ = g

2.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

3.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 16 of them exceeds 401 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 16> 401 kg

P =

4.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.1423. Find z to two decimals.

A = 0.1423

z =

5.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 90% of them lie (the 90th percentile).

μ = 178σ = 7P = 90%

x = cm

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 80% of them lie (the 80th percentile).

μ = 100σ = 15P = 80%

x = points

Answer key

1. σ = 9.849 g
2. σ = 2.5 min
3. P = 0.3085
4. z = 1.07
5. x = 187 cm
6. x = 112.6 points

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