Answer:
A sample size of 2401 is needed.
Explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the z-score that has a p-value of
.
The margin of error is given by:

95% confidence level
So
, z is the value of Z that has a p-value of
, so
.
What sample size would be needed to construct a margin of error of 2% with 95% confidence?
This is M for which n = 0.02.
Supposing we have no estimate for the true proportion, we use
.






A sample size of 2401 is needed.