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 0.1611. Find z to two decimals.

A = 0.1611

z =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.8315. Find z to two decimals.

A = 0.8315

z =

3.Medium

The masses of boxes are independent and normal with mean 12 kg and standard deviation 0.8 kg. Find the probability P that the total mass of 8 of them is below 100.5 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 8< 100.5 kg

P =

4.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 5 of them is below 204 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 5< 204 g

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 40% is to the right of it. Find the cut-off x.

μ = 65 pointsσ = 10 points40%

x = points

6.Hard

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.02 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.02 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.02 mm

P =

Answer key

1. z = −0.99
2. z = 0.96
3. P = 0.9767
4. P = 0.9319
5. x = 67.5 points
6. P = 0.7881

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