a radio station claims 55% of all listeners tune into their program between 8 and 9 am. To check this claim a competing radio station does a survey of a random sample of listeners in the 8 to 9 am time slot. the survey indicates the claim can not be rejected. if the sample size is 1000 people determine the least and greatest number of listeners that could of said they listen to the radio station.

this is what i have tried but i am not getting the right answer.

p=.55

using the margin of error formula. 1/ √1000 = .03126

so I would of thought the answer would be 1.55 +/- .03126 multiplied by a thousand. this does not give the right answer. the right answer is 519 to 581