What is the age of a 22 WMR Marlin 782 micro groove barrel serial 22755171?

1978 is the exact year.

To find the year of manufacture subtract the first two digits from 100, that will give you the year. Hence, 100 - 22 = 78, so that rifle was manufactured in 1978.

Marlin is still using this system currently so firearms made this year 2009, will start with the serial number 91, 100 - 09 = 91.