A vertical and horizontal collimation test for a total station was completed by sighting a distant point $4$ times direct and

$4$ times reverse.

a$.$ Average the readings.

b$.$ Compute the standard deviation $($in seconds$)$ of both direct and reverse zenith and horizontal circle readings.

c$.$ Compute the standard deviation in the mean $($in seconds$)$ of both direct and reverse zenith and horizontal circle

readings.

d$.$ Compute the collimation errors $($in seconds$)$ of both direct and reverse zenith and horizontal circle readings.

e$.$ Does the instrument have significant collimation error?