The population standard deviation for the scores of a standardized test is 4 points. If we want to be 90% confident that the sample mean is within 1 point of the true population mean, what is the minimum sample size that should be taken

The minimum sample size that should be taken is 44.

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.

If we want to be 90% confident that the sample mean is within 1 point of the true population mean, what is the minimum sample size that should be taken

This is n when . So

The minimum sample size that should be taken is 44.

f is the midpoint of