Converting DOB fromat

I have a table called NAMES that has a DOB column in nvarchar which for some reason will not convert to date, which is fine as long as I can run a snippet of code to convert it which is actually preferable. So here is the dilemma... some dates are m/d/yyyy and some are mm/dd/yyyy .

Examples:

2/4/1986
10/8/1999
4/24/1988
12/13/1975

I'd like to run a snippet of code to convert everything to a standard mm/dd/yyyy format. Thank you in advance...