According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. in a study conducted by researchers, 5 comma 000 roaches (the expected number in a roach-infested house) were released in the test kitchen. one week later, the kitchen was fumigated and 17 comma 468 dead roaches were counted, a gain of 12 comma 468 roaches for the 1-week period. assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.3. use the number of roaches produced by the sample of 5 comma 000 roaches to find a 90% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house.