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 0.8212. Find z to two decimals.

A = 0.8212

z =

2.Easy

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 118 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 118

P(X < x) =

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 5 of them is below 57.3 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 5< 57.3 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 16 of them exceeds 642.4 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 16> 642.4 g

P =

5.Hard

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. Find the value x below which 10% of them lie (the 10th percentile).

μ = 500σ = 40P = 10%

x = h

6.Hard

Hole diameters D are normal with mean 25.05 mm and standard deviation 0.015 mm. Shaft diameters d are independent and normal with mean 25 mm and standard deviation 0.015 mm. A randomly chosen shaft fits when D − d > 0. Find the probability P that it fits. Round z to two decimals.

hole: μ = 25.05 mm, σ = 0.015 mmshaft: μ = 25 mm, σ = 0.015 mm

P =

Answer key

1. z = 0.92
2. P(X < x) = 0.8849
3. P = 0.06552
4. P = 0.3085
5. x = 448.7 h
6. P = 0.9909

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