How the critical values was computed?

Hello Community,

In the “Critical Values” video of lecture 2 of week 4, I do not understand how the critical value k was calculated as shown in the screenshot. I watch this portion of the video several times but I feel like I am missing something. Can someone help me out here?

Thank You

To calculate critical value for Sample Mean with Sample Sigma known, we can use the following formulas:

Right tail : Xbar = mu(0) + Z(alpha)*Sigma(xbar)

Left tail : Xbar = mu(0) - Z(alpha)*Sigma(xbar)

2 sided : Xbar = mu(0) + Z(alpha/2)*Sigma(xbar)
Xbar = mu(0) - Z(alpha/2)*Sigma(xbar)

Hence:

k(0.05) = 66.7 +Z(0.05)(3/sqrt(10)
k(0.05) = 66.7 + 1.64
(0.95) = 68.26

Z(0.05) = Z subscript 0.05; don’t confuse it with multiplication; I don’t have subscript here.

Hope that’s clear.

How do we get Z(alpha) value and I am wondering why didn’t they include this process of calculation in the lecture? What am I missing?