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 179.4 cm? Find P(X > x) as a decimal.

μ = 178σ = 7x = 179.4

P(X > x) =

2.Easy

The exam scores are normally distributed with mean 65 points and standard deviation 10 points. What fraction is below 67 points? Find P(X < x) as a decimal.

μ = 65σ = 10x = 67

P(X < x) =

3.Medium

Drag z so that the shaded area under the standard normal curve, to the right of z, is 0.9319. Find z to two decimals.

A = 0.9319

z =

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 12 of them is below 482.1 g. Round z to two decimals.

μ = 40 gσ = 1.2 gn = 12< 482.1 g

P =

5.Hard

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. Find the value x below which 10% of them lie (the 10th percentile).

μ = 250σ = 5P = 10%

x = g

6.Hard

The mass X of a product from line 1 and Y from line 2 are independent and normal: X has mean 500 g and standard deviation 8 g, Y has mean 490 g and standard deviation 6 g. Find the probability P that X is greater than Y. Round z to two decimals.

μ_X = 500 g, σ_X = 8 gμ_Y = 490 g, σ_Y = 6 g

P =

Answer key

1. P(X > x) = 0.4207
2. P(X < x) = 0.5793
3. z = −1.49
4. P = 0.695
5. x = 243.6 g
6. P = 0.8413

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