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 battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 522 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 522

P(X > x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9788. Find z to two decimals.

A = 0.9788

z =

3.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 88.75 and 115.75 points? Give P as a decimal.

μ = 100σ = 15x₁ = 88.75x₂ = 115.75

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 197.3 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 5< 197.3 g

P =

5.Hard

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 10% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points10%

x = points

6.Hard

Hole diameters D are normal with mean 25.02 mm and standard deviation 0.01 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 = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm

P =

Answer key

1. P(X > x) = 0.2912
2. z = 2.03
3. P = 0.6265
4. P = 0.1562
5. x = 119.2 points
6. P = 0.8133

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