Question 1119721
sample size is 10.


standard error is standard deviation divided by square root of population size.


if you use z-scores, and it appears that you have to, since you don't know the mean or standard deviation of your population, your mean is 0 and your standard deviation is 1.


at 99.5% confidence level, 100% - 99.5% is your alpha.


that makes it equal to .5%.


divide that by 2 and you have half your alpha on the left end of the confidence interval and half on the right end.


that makes it 2.5% on each end.


2.5% is the same as .025 in decimal form.


look up a z-score to the left of .025 to get a z-score of -1.959963986 which can be rounded to -1.96.


since the normal distribution is symmetric about the mean, then your critical z-score is plus or minus 1.96.


that means .025 of the area under the normal distribution is to the left of -1.96 and .025 of the area under the normal distribution is to the right of 1.96.


that distribution would look like this.


inside the confidence interval:


<img src = "http://theo.x10hosting.com/2018/071802.jpg" alt="$$$" >


outside the confidence interval:


<img src = "http://theo.x10hosting.com/2018/071805.jpg" alt="$$$" >