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

X and Y are independent normal variables for the mass of a filled jar: jar plus contents: X has mean 250 g and standard deviation 4 g, Y has mean 500 g and standard deviation 9 g. Find the standard deviation σ of X + Y.

μ_X = 250 g, σ_X = 4 gμ_Y = 500 g, σ_Y = 9 g

σ = g

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.7190. Find z to two decimals.

A = 0.7190

z =

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 10 of them exceeds 401.9 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 10> 401.9 g

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 108.2 s. Round z to two decimals.

μ_X = 60, σ_X = 5μ_Y = 45, σ_Y = 4X + Y > 108.2 s

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 20% of them lie (the 20th percentile).

μ = 500σ = 40P = 20%

x = h

6.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Find the value x below which 75% of them lie (the 75th percentile).

μ = 65σ = 10P = 75%

x = points

Answer key

1. σ = 9.849 g
2. z = 0.58
3. P = 0.3085
4. P = 0.3085
5. x = 466.3 h
6. x = 71.75 points

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