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

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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.6217. Find z to two decimals.

A = 0.6217

z =

3.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 92.5 and 118.75 points? Give P as a decimal.

μ = 100σ = 15x₁ = 92.5x₂ = 118.75

P =

4.Medium

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 16 of them exceeds 190.4 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 16> 190.4 kg

P =

5.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 80% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points80%

x = points

6.Hard

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 99% of them lie (the 99th percentile).

μ = 32σ = 6P = 99%

x = min

Answer key

1. σ = 9.849 g
2. z = 0.31
3. P = 0.5858
4. P = 0.6915
5. x = 56.6 points
6. x = 45.96 min

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