Business and finance. 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 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? I am trying to figure it I divide 1/50 by the 24 hours
If he makes 20,000 per day that's 833.3 per hour.
if he samples 120 bottles an hour and its 1/50 of the sample that dictates the outcome (stop the line) then how many bottles is 1/50 of 120 ? That is of course if 'the line' talked about is one hours production.
If indeed the line is to mean a 24 hour period then it would be 1/50 of the amount of samples in a 24 hour period.
120 x 24 / 50
At the end of the day, are we talking about a one hour sample or a 24 hour sample?
To determine the number of defective bottles Julio should allow before rejecting the entire line, we can start by calculating the number of bottles he samples in a 24-hour period.
Julio samples 120 bottles per hour, so in 24 hours, he would sample:
120 bottles/hour * 24 hours = 2,880 bottles
Now, we need to calculate how many defective bottles would make Julio reject the line.
Julio finds the line defective if he finds more than 1/50 of the sample to be defective. In mathematical terms, this means more than 1/50 of the 2,880 bottles sampled.
To find out how many defective bottles he should allow, we can calculate 1/50th of the sample:
(1/50) * 2,880 = 57.6
Since we cannot have a fraction of a defective bottle, we round the result up to the nearest whole number. Therefore, Julio should allow 58 defective bottles before rejecting the entire line.