Modifying your jQuery side of things, you could do something like this:
$(document).ready(function(){
$(".hideme").hide();
$("#dropDownRange").change(function() {
if ($("#dropDownRange").val() == 'In Between')
$(".hideme").show();
else
$(".hideme").hide();
});
});
OnChange is added to the dropDownRange, as in your example the function is not being called.
In your html markup the hideme is specified as a class and not an id so use the period(.) to find it instead of the hash(#).