Using the z-distribution, it is found that the smallest sample size required to obtain the desired margin of error is of 4330.
<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:
- The estimate of the proportion is of
.
- The desired margin of error is of M = 0.01.
- 90% 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, the smallest sample size required to obtain the desired margin of error is of 4330.
To learn more about the z-distribution, you can take a look at brainly.com/question/12517818