How do I set up an Excel formula that calculates the percentage of "Y"
entries in a range of cells that contains both "Y" and "N" entries?

When I filled in Cells A1:C10 with various X's and Y's, this forumula worked:

=COUNTIF($A$1:$C$10,"Y")/COUNTIF($A$1:$C$10,"*")

It divides the number or cells containing Y by the number of cells
containing anything (but not blank).

If the range may include blanks that you want counted, try this:
=COUNTIF($A$1:$C$10,"Y")/(ROWS($A$1:$C$10)*COLUMNS($A$1:$C$10))

Note: In either case, you need to set the number format to Percent.

Does that help?

Regards,
Ron