According toscientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted byresearchers,5,000 roaches(the expected number in aroach-infested house) were released in the test kitchen. One weeklater, the kitchen was fumigated and18,486 dead roaches werecounted, a gain of13,486 roaches for the1-week period. Assume that none of the original roaches died during the1-week period and that the standard deviation ofx, the number of roaches produced per roach in a1-week period, is1.3. Use the number of roaches produced by the sample of5,000roaches to find a90% confidence interval for the mean number of roaches produced per week for each roach in a typicalroach-infested house.

Find a90%confidence interval for the mean number of roaches produced per week for each roach in a typicalroach-infested house.

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(Round to three decimal places asneeded.)