USING PROPORTIONS TO MAKE INFERENCES WORKSHEET

Problem 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?

Problem 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?

Problem 3 :

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

Problem 4 :

A manager samples the receipts of every fifth person who goes through the line. Out of 50 people, 4 had a mispriced item. If 600 people go to this store each day, how many people can we expect to have a mispriced item?

1. Answer :

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)/(3 ⋅ 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.

2. Answer :

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.

3. Answer :

6 is a little more than 10% of 50.

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

4. Answer :

Step 1 :

Set up a proportion.

Step 2 :

Substitute values into the proportion.

Substitute known values. Let x be the number of mispriced items in the population.

4/50 = x/600

Least common multiple of (50, 600) = 600.

So, multiply the numerator and denominator of the fraction 4/50 by 12.

(4 ⋅ 12)/(50 ⋅ 12) = x/600

48/600 = x/600

48 = x

Based on the sample, we can expect 48 mispriced items in the population of 600 people.

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