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 exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is above 77 points? Find P(X > x) as a decimal.

μ = 65σ = 10x = 77

P(X > x) =

2.Easy

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is below 53.5 points? Find P(X < x) as a decimal.

μ = 65σ = 10x = 53.5

P(X < x) =

3.Medium

The masses of bolts are independent and normal with mean 40 g and standard deviation 1.2 g. Find the probability P that the total mass of 12 of them is below 475.8 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 12< 475.8 g

P =

4.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 is below 401 kg. Round z to two decimals.

μ = 25 kgσ = 0.5 kgn = 16< 401 kg

P =

5.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 75% of them lie (the 75th percentile).

μ = 100σ = 15P = 75%

x = points

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) = 0.1151
2. P(X < x) = 0.1251
3. P = 0.1562
4. P = 0.6915
5. x = 110.1 points
6. P = 0.7389

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