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Using the z-distribution, as we are working with a proportion, it is found that samples of 937 should be taken.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
The margin of error is given by:
In this problem, we have that:
- The estimate is of
.
- The margin of error is of M = 0.03.
- 95% confidence level, hence
, z is the value of Z that has a p-value of
, so
.
Then, we solve for n to find the minimum sample size.
Rounding up, it is found that samples of 937 should be taken.
More can be learned about the z-distribution at brainly.com/question/25890103