I had purchased eggs at the supermarket and i forgot them in the trunk of my car for for 3 days are they still okay to eat?
They are probably OK as long as they didn't get too hot, but you should test them before eating. Here's how:
Fill a bowl with cold water and place an egg inside.
If it sinks to the bottom, it's good.
If it sinks but stands on its point, it's good, but won't be good for much longer and should be used soon.
If it floats, toss it.
As far as refrigerating eggs in the U.S. vs. European room temperature storage:
"In some European countries, egg-laying hens are vaccinated against salmonella. In the U.S., vaccination is not required, but eggs must be washed and refrigerated from farm to store, and producers must follow a host of other safety measures."
Why The U.S. Chills Its Eggs And Most Of The World Doesn't — September 11, 2014, Rae Ellen Bichell, NPR Eating And Health
Also, commercially produced American eggs are washed with soap and hot, steamy water after collecting which removes a thin protective layer from the shell, which can effect shelf life at room temp. As long as you use the water bowl test, you're good to go.