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

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is below 516 h? Find P(X < x) as a decimal.

μ = 500σ = 40x = 516

P(X < x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.0174. Find z to two decimals.

A = 0.0174

z =

3.Medium

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 98.6 s. Round z to two decimals.

μ_X = 60, σ_X = 5μ_Y = 45, σ_Y = 4X + Y > 98.6 s

P =

4.Medium

X is normal with mean 60 s and standard deviation 5 s; Y is independent and normal with mean 45 s and standard deviation 4 s. Find the probability P that X + Y is more than 114.6 s. Round z to two decimals.

μ_X = 60, σ_X = 5μ_Y = 45, σ_Y = 4X + Y > 114.6 s

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

μ = 250 gσ = 5 g95%

x = g

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 100σ = 15P = 99%

x = points

Answer key

1. P(X < x) = 0.6554
2. z = −2.11
3. P = 0.8413
4. P = 0.06681
5. x = 258.2 g
6. x = 134.9 points

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