Need Help on X stalling?

[eurogreek1]

I live in Colorado and just switched to my winter tires yesterday. When I picked up the X, it wouldn't start. I thought that they left the trunk open but didn't think twice after it was jumped. Later that night, went out and it wouldn't start again. Make a long story short, it didn't start again today so someone told me to go to Batteries Plus to check my battery before I buy a new one. I went and the guy checked my battery but right away, he said that my alternator was not working right. He said that it was pulling 11.1 and it should be pulling 13.1-13.3. I couldn't believe it so I would like to know if that is what the problem is. I have not changed my battery in a few years but I never expected the guy to say it was the alternator. Any advise would be great!