Problem $7-$ The grain size analysis for a soil is given as:

$\backslash$table$[[$Sieve No$.,$Grain Size $(mm),\%$ Passing$],[3^{\text{'}\text{'}},75,100],[{1\mathrm{.}5}^{?},38,70],[\frac{3}{4^{?}},19,49],[\frac{3}{8^{?}},9\mathrm{.}5,36],[$#$4,4\mathrm{.}75,27],[$#$10,2,20],[$#$40,0\mathrm{.}425,8],[$#$100,0\mathrm{.}15,5],[$#$200,0\mathrm{.}075,4]]$

a$)$ Plot a grain$-$size distribution curve.

b$)$ Determine $D_{10},D_{30},$ and $D_{60}$ from the grain$-$size distribution curve.

c$)$ Calculate the uniformity coefficient, $C_u.$

d$)$ Calculate the coefficient of curvature, $C_c.$

e$)$ Classify the soil using the USC System.