$12\mathrm{.}4$ For the leveling network shown in the accompanying figure, calculate

the most probable elevations for $x,Y,$ and $Z.$ The observed values and

line lengths are given in the table. Apply appropriate weights in the

computations.

FIGURE P$12\mathrm{.}4$

For Problem $12\mathrm{.}4,$ compute the reference standard deviation, and

tabulate the adjusted observations and their residuals.

Repeat Problem $12\mathrm{.}4$ and $12\mathrm{.}5$ using the following standard deviations

for the lines.

$($a$)$ Tabulate the most probable values for the adjusted bench marks.

$($b$)$ Tabulate the adjusted observations and their residuals.

$($c$)$ What is the reference standard deviation for the adjustment?