USING PROPORTIONS TO MAKE INFERENCES

Example 1 :

A shipment to a warehouse consists of 3,500 MP3 players. The manager chooses a random sample of 50 MP3 players and finds that 3 are defective. How many MP3 players in the shipment are likely to be defective?

Solution :

It is reasonable to make a prediction about the population, because this sample is random.

Step 1 :

Set up a proportion.

Step 2 :

Substitute values into the proportion.

Substitute known values. Let x be the number of defective  MP3 players in the population.

3/50 = x/3500

Least common multiple of (50, 70) = 3500.

So multiply the numerator and denominator of the fraction 3/50 by 70.

(3 ⋅ 70)/(50 ⋅ 70) = x/3500

210/3500 = x/3500

210 = x

Based on the sample, you can predict that 210 MP3 players in the shipment would be defective.

Example 2 :

Based on the information in question 1, how many MP3 players in the shipment can we predict to be damaged if 6 MP3s in the sample had been damaged?

Solution :

Step 1 :

Set up a proportion.

Step 2 :

Substitute values into the proportion.

Substitute known values. Let x be the number of defective  MP3 players in the population.

6/50 = x/3500

(6 ⋅ 70)/(50 ⋅ 70) = x/3500

420/3500 = x/3500

420 = x

Based on the sample, we can predict that 420 MP3 players in the shipment would be defective.

Example 3 :

How could we use estimation to check our answer for question 2 is reasonable?

Solution :

6 is a little more than 10% of 50

10% of 3,500 is 350, and 420 is a little more than that.

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