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 here.

Why we use Z aplha/2 instead of Z alpha ?

Confidence intervals are usually two-sided. In two-sided confidence intervals, we split alpha evenly into both tails, leaving alpha/2 in each tail. This implies that z_alpha/2 is the appropriate z value for the interval.