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 ifhe finds more than 1/50 of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?
if i take the 20,000 x by 1/50 i get 400 bottles or do i need to take the 120 that is done hourly and
120 x 1/50= 2 2/5. Please explain to me if I am doing this wrong
I read this problem as he rejects the line, whatever that line is. It is not explicit what he rejects.
In a sample, as you figured, 2.4 is 1/50 of the sample 120. So he accepts the "line" if two or less is defective, and he rejects the "line" if three or more is defective.
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?
To determine how many defective bottles Julio should allow before rejecting the entire line, we need to understand the sampling process and the acceptance criteria.
Julio samples about 120 bottles an hour. If he finds more than 1/50 of the sample to be defective, he rejects the line.
Let's break it down step by step:
1. Determine the size of the sample:
Julio samples 120 bottles an hour. We can assume that this hourly sample represents the entire production for that hour.
2. Calculate the acceptable number of defective bottles in the sample:
For each sample of 120 bottles, Julio would accept the sample if he finds two or fewer defective bottles (1/50 of 120 is 2.4, which we round down to 2).
3. Determine the total number of defective bottles that Julio should allow before rejecting the entire line:
Since Julio is monitoring a 24-hour production period, he needs to calculate the total number of defective bottles he can accept over the entire 24 hours.
To calculate this, multiply the number of acceptable defective bottles per sample by the number of samples taken in 24 hours:
2 defective bottles per sample x 24 hours = 48 defective bottles in 24 hours
Thus, Julio should allow up to 48 defective bottles before rejecting the entire line.
Please note that this assumes a proportional defect rate across all samples and may not account for other factors such as production fluctuations or additional quality checks beyond the sampling process.