Suppose Facebook has launched a new fact-checking feature. It conducts a survey among its user base, wherein it asks them the question 'Do you find the fact-checking feature useful?'. Out of the 2,500 respondents, 53.2% believe that the feature is useful. If you define X as the proportion of people that find the feature useful, the frequency distribution for X would be as shown in the table given below.

X	Frequency
1	1,330
0	1,170

Sampling and Estimation

Suppose the population standard deviation is known to be 0.6, what is the interval in which the mean of the sampling distribution of sample size 2,500 will belong at a 99% confidence level?

(0.456, 0.608)

(0.572, 0.588)

(0.493, 0.571)

(0.501, 0.563)