Here is another one that I am having trouble with.

Julio works as a quality control expert in a beverage factory.The assembly line that he monitors produces about 20,000 bottles in a 24-hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?

Again, I do not want the ANSWER, I need to understand the equation to use to solve it.

1/50 * 120 = ?

or
0.02 * 120 = ?

2.40 i think

Right. So when Julio finds the third defective bottle in his sample, he needs to reject the entire line.

To solve this problem, we can use the concept of proportion. Let's break down the information we have:

- Julio samples 120 bottles per hour.
- He rejects the line if more than 1/50 of the sample is defective.
- The production line produces 20,000 bottles in a 24-hour period.

To find out how many defective bottles Julio should allow before rejecting the entire line, we need to determine the maximum number of defective bottles per sample that would still meet the criteria for rejection.

First, let's find the number of bottles Julio samples in a 24-hour period. Since he samples 120 bottles per hour, in 24 hours he will sample:

120 bottles/hour * 24 hours = 2,880 bottles.

Now, let's determine the maximum number of defective bottles in a sample that would not exceed the rejection criteria. We know that Julio rejects the line if he finds more than 1/50 (or 1 divided by 50) of the sample to be defective. Therefore, the maximum allowable number of defective bottles in a sample can be calculated as:

2,880 bottles * (1/50) = 57.6.

However, since we can't have a fraction of a bottle, we need to round up to the nearest whole number. Thus, the maximum number of defective bottles in a sample that Julio should allow before rejecting the entire line is 58.

So, Julio should allow a maximum of 58 defective bottles in a single sample before deciding to reject the entire line.