Q. Is there a website or source to check the on-time schedule for various airlines? I'm trying to make a reservation and I'm given a 38 minute layover to make a Delta connection in Detroit. Is this even possible? 

A. Only 38 minutes? Eeek. Sure, it's possible, but that doesn't allow you much wiggle room for any little thing that might (and often does) go wrong. Hopefully, you'll arrive within a short walk to the gate for your connecting flight.

As for a site that allows you to check on-time statistics, there does exist such a thing. The US Department of Transportation Bureau of Statistics allows you to track on-time statistics by airline, airport and flight number. If your flight has a lousy on-time track record, you might try pointing out your skimpy connection time to a Delta agent and plead to be switched to an earlier flight without having to cough up the change fee.