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

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 124 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 124

P(X < x) =

2.Easy

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is above 112 points? Find P(X > x) as a decimal.

μ = 100σ = 15x = 112

P(X > x) =

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 398 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 16> 398 kg

P =

4.Medium

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction lies between 53.5 and 75 points? Give P as a decimal.

μ = 65σ = 10x₁ = 53.5x₂ = 75

P =

5.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Drag the cut-off so the shaded top 70% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g70%

x = g

6.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Drag the cut-off so the shaded bottom 30% is to the left of it. Find the cut-off x.

μ = 500 hσ = 40 h30%

x = h

Answer key

1. P(X < x) = 0.9452
2. P(X > x) = 0.2119
3. P = 0.8413
4. P = 0.7163
5. x = 247.4 g
6. x = 479 h

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