Determine the sample size needed to construct a 95% confidence interval to estimate the average GPA for the student population at a colege with a margin of error equal to 0.03. assume the standard deviation of the GPA is 2.0

The sample size needed is at least 17,074 students.

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, 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.

Sample size:

At least n, in which N is found when . So

The sample size needed is at least 17,074 students.

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