6)

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 mach-infested house} were released in the test kitchen. One weelc later, the Idtchen was fumigated and 14,26 dead roaches were counted. a gain of 10,226 reaches for the 1-week period. Assume that none of the original roaches died during the theelc period and that the standard deviation of x, the number of roaches produced per roach in a 1week period, is 1.4. Use the number of roaches produced by the sample of 4,000 reaches to nd a 90% condenoe interval for the mean number of reaches produced per week for each mach in a typical roach-infested house. Find a 90% condence interval for the mean number of roaches produced per week for each reach in a typical roactHntested house. (DD) (Round to three decimal places as needed.)