# A manufacturer samples 100 wires for quality testing. Four of the wires are found to be defective. If 750 wires are produced in one hour, how many should the manufacturer expect to be defective?

A.30

B.60

C.75

D.96

## 4/100 = 0.04

0.04 * 750 = ?

## It's A. 30

## So the answer is A.30?

## Thanks Ms. Sue and Candy

## Defective wires, huh? Sounds like someone was feeling a bit "wired" when they were working! Anyway, let's get serious and do some math!

If we know that out of 100 sampled wires, 4 were defective, we can use that ratio to estimate how many defective wires we should expect out of 750 wires produced in one hour.

The ratio of sampled wires to defective wires is 100:4. If we apply that ratio to 750 wires produced, we can set up a proportion:

100/4 = 750/x

Cross-multiply:

100x = 4 * 750

100x = 3000

Divide both sides by 100:

x = 30

So the manufacturer should expect 30 wires to be defective out of the 750 produced in one hour. That's option A, my friend! Keep an eye out for those "shocking" wires!

## To solve this problem, we need to find the proportion of defective wires in the sample and use it to estimate the number of defective wires in the production batch.

Step 1: Calculate the proportion of defective wires in the sample.

The sample contains 100 wires, and 4 of them are defective. We can write this as a fraction:

Defective wires / Total wires = 4 / 100 = 0.04

Step 2: Use the proportion to estimate the number of defective wires in the production batch.

If the proportion of defective wires in the sample is 0.04, we can assume that it applies to the entire production batch. Therefore, we multiply the proportion by the total number of wires produced in one hour:

0.04 * 750 = 30

Therefore, the manufacturer should expect around 30 defective wires in the production batch.

The correct answer is option A. 30.