No, it's not OK. It's never OK to be "running late" according to however that is locally defined. Even at a place that says, "We don't care when you come in or

No, it's not OK. It's never OK to be "running late" according to however that is locally defined. Even at a place that says, "We don't care when you come in or work at home, just as long as you're on site once a week on Wednesdays from noon to 3 pm," if you show up every Wednesday at 12:30 pm instead of at 12:00, your boss will get annoyed with you. If there was a particular reason why you needed to come in at 9:05 instead of 9:00 every day, for example a bus schedule, that is a reasonable thing to negotiate. The correct professional behavior (in ANY industry) is almost never to just ignore what your boss asks you repeatedly to do. The best thing when confronted by something like this is to openly discuss and negotiate the issue. If you were sent home for the whole day, that sounds like a last warning at the end of a long series of failures to follow the customs of that particular company. If you don't come in on time on Monday, I suspect you will be fired immediately.