Combining the suggestions of @wch1pink, @Mockman and @Ted Wrigley here are two approaches:
set AppFolder to path to applications folder
set NumLoc to AppFolder & "Numbers.app" as string
try
NumLoc as alias
set NumExists to true
on error
set NumExists to false
end try
The setting of the variable is just for illustration. Or more directly:
if exists application "Numbers" then
set NumExists to true
else
set NumExists to false
end if