**Using proportions to make inferences worksheet :**

Worksheet on using proportions to make inferences is much useful to the students who would like to practice problems on proportions.

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 ?

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 ?

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

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 ?

**Question 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

50 x 70 = 3500, so multiply the numerator and denominator of the fraction 3/50 by 70.

(3x70) / (50x70) = 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.

**Question 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

50 x 70 = 3500, so multiply the numerator and denominator of the fraction 6/50 by 70.

(6x70) / (50x70) = 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.

**Question 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.

**Question 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 ?

**Solution :**

**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

50 x 12 = 600, so multiply the numerator and denominator of the fraction 4/50 by 12.

(4x12) / (50x12) = x / 600

48 / 600 = x / 600

48 = x

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

After having gone through the stuff given above, we hope that the students would have understood "Using proportions to make inferences worksheet".

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