t and z as mentioned above are multipliers that determine how many standard errors wide our margin of error will be for a desired confidence level.
When estimating the population mean mu with a small sample size (n<=40), the statistic (barX-mu)/sigma is assumed to come from a t distribution with n-1 degrees of freedom (d.f.). This is when we use t_(alpha//2," " n–1).
The family of t distributions looks similar to the standard normal z distribution, but with heavier tails. As the sample size n increases, the t_(n–1) distribution approaches the z distribution.
When the sample size is sufficiently large (i.e. >40), the t distribution (with n-1 d.f.) and the z distribution are approximately equivalent, so it is widely accepted to use the z distribution when n>40.
For an 85% C.I., we have alpha = 0.15. Assuming your sample size is large enough, you would multiply the standard error sigma/sqrtn for the mean mu by
z_(alpha//2) = z_(0.15//2)=z_0.075~~1.44
This value of 1.44 can be found by reverse-lookup in a z-table, or with Statistics software.
