where did they get 2.05 ?

Question

a simple randon sample of size n is drawn from a population that is normally distrobuted with population standeard deviation is known to be 13 the sample mean x with a line above it is found to be 108

compute the 96 % confidence intervial about mean if the sample size is 25.
the first part of the answer is 108-2.05. where did they get 2.05 ?

mtg how would i get the number useing a calculator ? i have a ti-89

Answer 1

The 2.05 was obtained from a standard normal z-table for a 96% confidence interval when the standard deviation is KNOWN.
The formula for a 96% confidence limit is
Xbar ± zα/2(s/√n)
Where zα/2 = 2.05 from the standard normal table for area (probability) = 0.02 in each tail.
Evaluating:
108 ± 2.05(13/√25)
And the interval is:
102.67 < µ < 113.33

Answer 2

must have something to do with the z statistic

the confidence interval means mean+/- z*standard deviation

since u need the 96% CI the corresponding z value turns out to be 2.05 (i verified this from the table)

hence u get 2.05

Answer 3

My guess is that that is the Z-value corresponding to a 96 percent confidence interval.