All you need to do to change @Georg formula to output the 15th day instead of the 1st day, is to change the Day parameter passed to the Date DMY() function. This would be the first parameter, as indicated in the name of the function. As can be seen in @Georg formula, the value is "1". Just change it to 15.
The changing of the display format to m/d/y, what needs to be done, is to go to the Column Info dialog box(right click on the column header and select Column Info), and in that dialog, change the format to the m/d/y format.
Documentation on JMP date time columns is covered in the JMP Document called Using JMP. It can be found in the JMP Documentation Library, available under the Help pull down menu.
Jim