Does your 11 year old scream at people? If so, your 3 year old is only imitating what she sees. If there are any other adults that your daughter comes in contact with that yell ans scream most of the time, then your daughter is only imitating them as well.
When you do ask her a question and she responds in a loud and screaming manner, simply tell her that you really are interested and concerned with what she has to say but you would like for her to speak in an inside quiet voice. Show her the difference between a loud voice and an inside quiet voice. When you are explaining the difference, get right down to her eye level when you talk to her.
Then the nest time she yells, go up to her and say, ("Susie")...I would appreciate it if you could lower your voice and let me know what you need. Remember we talked about an inside voice?
Then when she starts using an inside voice on a continuous basis, reward her GREAT BEHAVIOR with a sticker on a calendar or simple index card. When she has had a great day of no yelling, she will receive a sticker for that day. After 10 stickers (you can alter the amount), then reward her good behavior with a fun activity or a treat. Make sure she knows beforehand what she is working towards. Your focus is on her positive behavior. This may take a little while before she gets the hang of it but it will work. The key is patience and persistence.
Have a great day!!!!