Cooking a 2.5 lb prime rib takes around 3 hours to 3 and 1/2 hours depending on how well done you want the prime rib to be cooked.
For me 3 and 1/2 hours is good enough for me when cooking a 2.5 lb prime rib but you might want your prime rib less done or more well done.
Make sure the internal temperature of the prime rib is at least 120 degrees F if you have a meat thermometer.
You should preheat the oven to 250 degrees F and then keep the oven at 250 degrees F for the 3 hours and keep check on the prime rib after a few hours.