The soil from Problem $1$ is used in the construction of an embankment. The specification for compaction states that the compacted field soil must be at least $\backslash (98\backslash \%\backslash )$ of the maximum dry unit weight, and within $\backslash (+/-2\backslash \%\backslash )$ of the optimum water content for the standard compaction curve. In the field, a sand cone test was performed to determine the quality of the field compaction. A hole was dug in the compacted soil to collect a sample that weighs $5\mathrm{.}283$ lbs wet and $4\mathrm{.}675$ lbs dry. Then, the hole was filled by the Ottawa sand. The collected data are given below:

$*$Note: the standard energy laboratory compaction test on the soil is shown in Problem $1.$

a$)$ What is the dry compacted unit weight and water content of the compacted lift? What is the percent compaction $($Relative Compaction$)?$ Does the sample meet the specifications?

b$)$ What is the compacted degree of saturation?

c$)$ If the compacted sample were saturated, what would the water content be$?$