According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 4,000 roaches the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 15,400 dead roaches were counted, again of 11,400 roaches for the 1-week period. Assume that none of the original roaches died during
the 1-wook period and that the standard deviation of 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 4,000 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.
Find a 90% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infosted house.
(Round to three decimal places as needed.)