Is the passage of dialogue written correctly or incorrectly?

Question

anonymous · Answer

wheres the dialogue?

anonymous · Answer

"Is anyone here allergic to peanuts?" asked Ms. Williams. 
    "I am," said Taylor. 
    "I'm not, but I don't like them," offered Stan. 
    Ms. Williams said, "Well then, we won't have peanut butter and jelly sandwiches for lunch. How about grilled cheese?" 
    "Sure!" said Stan and Taylor. "I'm allergic to dairy products," piped up Nina. 
    "We'll think of something!!" said Ms. Williams.

anonymous · Answer

i think its written incorrectly because there are commas after some replies when there are supposed to be periods.

anonymous · Answer

Thank you, that's what I thought too!

anonymous · Answer

your welcome c: