How to find the probability of a sampling error made in estimating the population mean?

Alright, I have been working on my statistics assignment since Monday and I only have two questions left, dealing with the probability of a sampling error. Unfortunately, I cannot find anything in my notes and only a brief example in my textbook that does not explain the concepts behind the answer. I'm going to post the question below for clarification but I was hoping for a bit of an explanation so that I can figure out my second question on my own!

mean = 6.74 million standard deviations = 15.37 million variable is known to have a right-skewed distribution
What is the probability that the sampling error made in estimating the population mean loan amount by the mean loan amount of a simple random sample of 200 loans will be at most 1 million?

I figured it has to do something with z-scores but that as far as I got as I do not understand how to do this problem at all! Thank you for the help!


Omega Contributor
Yeah these are tricking given wording. I would if you had a null hypothesis that the sample mean equals the population means if the respective pvalue for having a sample mean the large or larger would translate to what they are calling a sampling error.

Yes, traditionally when you are dealing also with the population values you use z-scores.
thank you for your reply! so how would i find the z-score since i am not given an x? the only formula i know for finding z-scores is subtracting x by the mean and dividing that by the standard deviation. my professor hasn't gone over anything about p-values or null hypothesis either so i'm not sure how to proceed with that approach