Formula to Average if at least X cells have values

I have sets of student scores where one student may only have one score, but another may have 6. I'm looking for a formula that will average the scores only if the student has at least 4, but they could be anywhere in the row. I've gotten it to work where it will not average the score if one value is missing, using a simple IF-AND, but then I lose students with 4 or 5 scores. Any ideas? Thanks!

See attachment below. If it matters, the way the sheet is set up, those blank cells aren't really blank, but are errors that return a "" value.

average formula sample.xlsx

Beauty. Thank you much!