what is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E=1.5? The population standard deviation is known to be 10.75

The minimum sample size is 198

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.

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E=1.5?

This sample size is n.

n is found when M = 1.5.

We have that

Rounding up

The minimum sample size is 198

we need more info to solve this