I derive the appropriate formula for a confidence interval for the population mean mu, when sampling from a normally distributed population with a known value of sigma.
(The purpose of this video is to show the rationale behind the confidence interval formula for mu.) I do not work through an example in this video; I work through an example in    • Confidence Intervals for One Mean:  S...  .

For those that use R, here is the R code to find some of the values used in the video:

P(-1.96 less than Z less than 1.96), where Z is a standard normal random variable:
pnorm(1.96) - pnorm(-1.96)
[1] 0.9500042

Finding the z value with 0.25 of an area to the left:
qnorm(.025)
[1] -1.959964

Finding the z value with 0.25 of an area to the right:
qnorm(.975)
[1] 1.959964