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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9821. Find z to two decimals.

A = 0.9821

z =

2.Easy

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is below 67 points? Find P(X < x) as a decimal.

μ = 65σ = 10x = 67

P(X < x) =

3.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 187.2 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 16> 187.2 kg

P =

4.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 85.75 and 122.5 points? Give P as a decimal.

μ = 100σ = 15x₁ = 85.75x₂ = 122.5

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 bottom 95% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h95%

x = h

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 20% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points20%

x = points

Answer key

1. z = 2.1
2. P(X < x) = 0.5793
3. P = 0.9332
4. P = 0.7621
5. x = 566 h
6. x = 112.6 points

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