$4\mathrm{.}1$ Results from liquid and plastic limit tests conducted on a soil are given here.

Liquid limit tests:

$\backslash$table$[[$Number of blows, $N,$Moisture content $(\%)],[14,38\mathrm{.}4],[16,36\mathrm{.}5],[20,33\mathrm{.}1],[28,27\mathrm{.}0]]$

Plastic limit tests: $PL=13\mathrm{.}4\%$

a$.$ Draw the flow curve and obtain the liquid limit$.$

b$.$ What is the plasticity index of the soil?

$4\mathrm{.}2$ Determine the liquidity index of the soil in Problem $4\mathrm{.}1$ if $w_{in\text{s}\text{i}\text{t}\text{u}}=32\%.$