Thanks - removed it.

The の is indeed optional. The の is used in instances where you're trying to ascertain more detailed information pertaining to your question.

I have just been told by a Japanese English teacher that this grammar construction would only ever be used in written Japanese, and even in written Japanese, women would never use it. Apparently, it is not used in conversations by either men or women.

So, in conversation, the sentence 本当に出来るのかい？ would become 本当に出来るの？ or 本当に出来る？

I hear it all the time on アニメ. I know that's probably not the corroborative source you were looking for, but there it is. Most of the time I see it used by middle-aged to elderly people (both men and women, but probably more by the former), especially when they are speaking in a kind tone to younger people or children. I've also seen it in 漫画, in similar situations. Here's what [i]Japanese: The Manga Way[/i] has to say about it: "In colloquial speech, かい is sometimes used instead of か to mark a question. Most commonly it has a softer, friendlier feeling than the abrupt か, but the right tone of voice in a contentious situation can make it even more forceful than か."

I've seen it used by both women and men when chatting. I use it myself (girl).