Answer:
We need a sample size of at least 1161.
Step-by-step 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 zscore that has a pvalue of
.
The margin of error for the interval is:

For this problem, we have that:

90% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
How large a sample should she take?
We need a sample size of at least n.
n is found when 
So






Rounding up
We need a sample size of at least 1161.