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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1.Easy

The heights of adult men are normally distributed with mean 178 cm and standard deviation 7 cm. What fraction is above 190.6 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 190.6

P(X > x) =

2.Easy

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction is below 256 g? Find P(X < x) as a decimal.

μ = 250σ = 5x = 256

P(X < x) =

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.7881. Find z to two decimals.

A = 0.7881

z =

4.Medium

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. What fraction lies between 76.75 and 107.5 points? Give P as a decimal.

μ = 100σ = 15x₁ = 76.75x₂ = 107.5

P =

5.Hard

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. Find the value x below which 95% of them lie (the 95th percentile).

μ = 32σ = 6P = 95%

x = min

6.Hard

Hole diameters D are normal with mean 25.05 mm and standard deviation 0.02 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 = 0.02 mmshaft: μ = 25 mm, σ = 0.015 mm

P =

Answer key

1. P(X > x) = 0.03593
2. P(X < x) = 0.8849
3. z = −0.8
4. P = 0.6309
5. x = 41.87 min
6. P = 0.9772

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