Suppose the heights of seasonal pine saplings are normally distributed. If the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean?

The minimum sample size needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean is 47.

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 the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean?

This is n when . So

The minimum sample size needed to be 95% confident that the sample mean is within 4 millimeters of the true population mean is 47.