Melanie, I think you even asked something about losing over 50 pounds in 2 months (an even longer time ago). Before you even begin your journey, it's very important to have a realistic perspective about weight loss. If you expect big losses, and you don't get them, you may use it as a reason to give up. Don't be overly concerned about "how much weight can I lose in
x amount of time." We all like to have the weight come off quickly, but as you get smaller, and the weight comes off even slower, you'll have to accept the fact that patience (along with persistence) are more important factors to get to your goal weight than having to "beat the clock."
And to answer your question, it is possible to healthfully lose 15 pounds in one month IF you have a LOT of weight to lose. I lost 20 pounds my first month, but I was over 300. I couldn't imagine losing that now -- I've lost 2 pounds in the past 3 months. I'm disappointed, but I know now my body physically can't lose its excess weight rapidly anymore, and I've come to terms with that.