A distance $AB$ is observed repeatedly using the same equipment and procedures, and the results, in feet, are listed below. Calculate $($a$)$ the lines most probable length, $($b$)$ the standard deviation, and $($c$)$ the standard deviation of the mean for the set of results.

Carry out your final answers to $4$ significant digits $($decimal places$).$

$\backslash$table$[[$Measurement$,$Length$],[,($m$)],[1,65\mathrm{.}4010],[2,65\mathrm{.}4000],[3,65\mathrm{.}4020],[4,65\mathrm{.}3960],[5,65\mathrm{.}4060],[6,65\mathrm{.}4010],[7,65\mathrm{.}3960],[8,65\mathrm{.}4010],[9,65\mathrm{.}3905],[10,65\mathrm{.}4040],[11,65\mathrm{.}4080],[12,65\mathrm{.}4090]]$

In problem #$1,$ determine the range $($to $4$ decimal places$)$ within which observations should fall $($a$)90\%$ of the time and $($b$)95\%$ of the time. List the percentage of values that fall within these ranges.

What is the area of a rectangular field and its estimated error in area for the following recorded values?

$($a$)243\mathrm{.}89+-0\mathrm{.}05ft$ by $208\mathrm{.}65+-0\mathrm{.}04ft$

$($b$)725\mathrm{.}33+-0\mathrm{.}08ft$ by $664\mathrm{.}21+-0\mathrm{.}06ft$

$($c$)128\mathrm{.}526+-0\mathrm{.}005m$ by $180\mathrm{.}403+-0\mathrm{.}007m$

Give answers to the following problems in the correct number of significant figures using the rules of rounding:

$($a$)$ Sum of $0\mathrm{.}22,3\mathrm{.}1496,2\mathrm{.}2,$ and $541\mathrm{.}4586$

$($b$)$ Result of $9\mathrm{.}543-10\mathrm{.}75+247\mathrm{.}1425$

$($c$)$ Product of $2\mathrm{.}4583\mathrm{.}940\mathrm{.}46$

$($d$)$ Result of $\frac{45\mathrm{.}3440\mathrm{.}42}{0\mathrm{.}6}$