$9\mathrm{.}14$ As a materials engineer working for a highway department, what standard PG asphalt binder grade would you specify for each of the conditions shown in $($show all calculations and fill in the table$)?$

Table P$9\mathrm{.}14$

$\backslash$table$[[$Seven$-$Day Maximum Pavement Temperature,Minimum Pavement Temperature,Recommended PG Grade,$],[$Case $,$Mean, $C,$Standard Deviation, $C,$Mean, $C,$Standard Deviation, $C,50\%$ Reliability,$98\%$ Reliability$],[1,43,1\mathrm{.}5,-29,2\mathrm{.}5,,],[2,51,3,-18,4,,],[3,62,2\mathrm{.}5,10,2,,]]$