Conditional Formatting not working properly - not highlighting cells correctly

The attached sample spreadsheet shows a few different formulas and conditional formatting, but I have a question that is specifically related to the conditional formatting in Column C, which is not working properly for some reason. I left the other formulas/formatting in the sample in case those be the problem.

I would like to format as follows in Column C using the "days" values in Column D

days that are greater than or equal to 15 and less than or equal to 26 highlight "YELLOW"
days that are greater than or equal to 27 highlight "RED"
Cells that are blank, or less than 15 "no formatting"

Day values that are 14 are showing yellow highlights, one cell with 33 days shows no formatting, etc. I realize that I did not add into the spreadsheet formula the "equal to," but want to do that as well.

What am I doing wrong?

Thank you