Here is my question: 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?
1/50 * 120 = 2 2/5
Since he needs to find more than 2 2/5 defective bottles, he should reject the entire line when he finds that 3 are defective.
To determine the maximum number of defective bottles that Julio should allow before rejecting the entire line, we need to follow these steps:
Step 1: Calculate the total number of bottles that Julio samples in a 24-hour period.
Since Julio samples 120 bottles per hour, we can calculate the total number of bottles he samples in 24 hours by multiplying the number of bottles sampled per hour (120) by the number of hours in a day (24):
Total bottles sampled = 120 bottles/hour * 24 hours = 2,880 bottles.
Step 2: Determine the threshold for the maximum number of defective bottles allowed in the sample.
According to the information provided, if Julio finds more than 1/50 of the sample to be defective, he should reject the line. To calculate this threshold, we divide the total number of bottles sampled by 50:
Threshold = Total bottles sampled / 50 = 2,880 bottles / 50 = 57.6 bottles.
Step 3: Round the threshold to a whole number.
Since we cannot have a fraction of a bottle, we need to round the threshold number up to the nearest whole number. In this case, we round 57.6 up to 58 bottles.
Therefore, Julio should allow a maximum of 58 defective bottles before rejecting the entire line.