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

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.1401. Find z to two decimals.

A = 0.1401

z =

2.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

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 4 of them exceeds 162.4 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 4> 162.4 g

P =

4.Medium

X is normal with mean 12 min and standard deviation 1.5 min; Y is independent and normal with mean 20 min and standard deviation 2 min. Find the probability P that X + Y is more than 34 min. Round z to two decimals.

μ_X = 12, σ_X = 1.5μ_Y = 20, σ_Y = 2X + Y > 34 min

P =

5.Hard

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. Drag the cut-off so the shaded top 95% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points95%

x = points

6.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 30% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points30%

x = points

Answer key

1. z = −1.08
2. σ = 9.849 g
3. P = 0.1587
4. P = 0.2119
5. x = 48.6 points
6. x = 107.8 points

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