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?
I know we are supposed to estimate, but I am very confused about the problem. Pplease help me by showing your work.
1/50 * 120 = ?
so would it be 3 bottles an hour, so around 72 bottles?
1/50 * 120 = 120/50 = 2.4
About how many defective
bottles should Julio allow before rejecting the entire line?
He should allow only 2 defective before he rejects the entire line.
To find the approximate number of defective bottles that Julio should allow before rejecting the entire line, we can follow these steps:
Step 1: Calculate the total number of bottles Julio samples in a 24-hour period.
Since Julio samples 120 bottles per hour, he would sample 120 bottles × 24 hours = 2,880 bottles in a 24-hour period.
Step 2: Determine the maximum number of defective bottles Julio can tolerate in his sample.
Julio rejects the line if he finds more than 1/50 of the sample to be defective. So, the maximum number of defective bottles Julio can tolerate is 2,880 bottles × 1/50 = 57.6 bottles.
Step 3: Round the maximum number of defective bottles to a whole number.
Julio cannot have a fraction of a defective bottle, so we need to round the maximum number of defective bottles to the nearest whole number. In this case, 57.6 bottles would round up to 58 bottles.
Therefore, Julio should allow a maximum of 58 defective bottles before rejecting the entire line.