If you could include how you get to the answer that would be

If you could include how you get to the answer that would be great, thank you!

In constructing 95% confidence intervals for means, over the long run, about what percentage of the time would each of the following happen? The distance between the sample mean and the population mean is less than the margin of error The distance between the sample mean and the population mean is more than the margin of error

Solution

a) 95% of times and b) 5% of time.

95% CI means that the procedure we used is such that the CI created from random sample includes mean 95% of the time, which is same as saying that population mean and sample mean are less than margin of error apart 95% of time, and they are more than MoE apart 5% of the time.