$10\mathrm{.}1$: An angle was measured as $56\backslash$deg $1500$ using an engineer$$s transit, and had a standard deviation of $\backslash$pm $30.$ It was measured again using a repeating optical theodolite as $56\backslash$deg $1444$ with a standard deviation of $\backslash$pm $10.$ This angle was measured a third time with a directional theodolite $56\backslash$deg $1448$ with a standard deviation of $\backslash$pm $5.$ Calculate the weighted mean of the angle and its standard deviation $($Equation $10\mathrm{.}20).$

$10\mathrm{.}2$: What is the standard deviation of the weighted mean for Problem $10\mathrm{.}1?$