What should a size of a sample be in order to have a margin of error of 4% for a 90% confidence level from a population with a standard deviation of 35?

We need a sample size of 2,071,800 or higher.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, we find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

In this problem:

We need a sample size of n or higher, when . So

We need a sample size of 2,071,800 or higher.