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 IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction is below 103.75 points? Find P(X < x) as a decimal.

μ = 100σ = 15x = 103.75

P(X < x) =

2.Easy

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9429. Find z to two decimals.

A = 0.9429

z =

3.Medium

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction lies between 171 and 192 cm? Give P as a decimal.

μ = 178σ = 7x₁ = 171x₂ = 192

P =

4.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 9 of them exceeds 110.4 kg. Round z to two decimals.

μ = 12 kgσ = 0.8 kgn = 9> 110.4 kg

P =

5.Hard

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. Find the value x below which 99% of them lie (the 99th percentile).

μ = 178σ = 7P = 99%

x = cm

6.Hard

Hole diameters D are normal with mean 25.03 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 = 25.03 mm, σ = 0.01 mmshaft: μ = 25 mm, σ = 0.02 mm

P =

Answer key

1. P(X < x) = 0.5987
2. z = 1.58
3. P = 0.8186
4. P = 0.1587
5. x = 194.3 cm
6. P = 0.9099

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