Amy works for a company that produces plastic lids and cups for restaurants. She wants to estimate what proportion of lids produced in a day have a defect that makes them not fit the cups. She takes a random sample of 250250250 lids from the more than 10{,}00010,00010, comma, 000 total lids produced that day and finds 151515 lids in the sample with this defect. Based on this sample, which of the following is a 99\%99%99, percent confidence interval for the proportion of lids produced that day with this defect?.