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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 127.75 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 127.75

P(X < x) =

2.Easy

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 572 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 572

P(X > x) =

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.2236. Find z to two decimals.

A = 0.2236

z =

4.Medium

The masses of passengers with luggage are independent and normal with mean 85 kg and standard deviation 12 kg. Find the probability P that the total mass of 12 of them is below 978.4 kg. Round z to two decimals.

μ = 85 kgσ = 12 kgn = 12< 978.4 kg

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 85% is to the right of it. Find the cut-off x.

μ = 250 gσ = 5 g85%

x = g

6.Hard

The heights X of men and Y of women in a group are independent and normal: X has mean 180 cm and standard deviation 10 cm, Y has mean 170 cm and standard deviation 12 cm. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 180 cm, σ_X = 10 cmμ_Y = 170 cm, σ_Y = 12 cm

P =

Answer key

1. P(X < x) = 0.9678
2. P(X > x) = 0.03593
3. z = 0.76
4. P = 0.1587
5. x = 244.8 g
6. P = 0.7389

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