Question

6. 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? (1 point)
HINT: Again, we will write and solve a proportion. We know a that 4 of 100 wires were found to be defective. Based on this, if we test 750 wires, how many will be defective?
• 30
• 75
• 96

Answer 1

We looked 100 wires, and 4 were defective. How many more defective wires would you expect to see if we looked at another 100 wires?

Answer 2

You'd expect another 4, of course, giving a total of 8 defective wires out of a sample of 200. We're assuming that the number of defective wires is a constant percentage of the number of wires made, which is probably okay if you make a lot of wires, and might not be if you just make a few. But as this isn't a statistics problem, let's ignore that little quibble :-)

We have a ratio here: 4 defective wires per 100 wires sampled, or 4:100, or \(\frac{4}{100}\). That means we can set up a proportion to find the expected number of defective wires in a different sample size:

\[\frac{4}{100} = \frac{\text{defective}}{\text{sampled}}\]

Now we just plug in the new sample size for "sampled", and solve for "defective" by cross-multiplication.

Answer 3

Because you are given answer choices to choose from, rather than being required to actually find the answer yourself, you could also make a selection by noting that 750 is 700+50, and that for each 100 wires, you expect 4 defective wires. You've got 7 100s + 1/2 a 100, so if each of those 100s contributes 4 defective wires, how many defective wires is that? Then add half of 4 to represent the contribution of the sample of 50 wires (because 50 is 1/2 of 100). Be sure to work the problem with the proportion as requested, but then check your answer by doing it this way.