$0\mathrm{.}2$

An initial charge of particle $($A$)$ of $400g$ is mixed with $600g$ of particle $($B$)$ in a reactor. After $1$ minute of mixing $5$ spot samples, each containing an average number of particles about $50$ particles, for the evaluation of the performance of the mixture, calculate:

$($a$)$ The standard deviation

$($b$)$ The mixing index $I_s$

$($c$)$ The least value of the mixing index Is$.$o$.$

$($d$)$ The mixing index after a time of $150$ seconds.

$\backslash$table$[[$Sample No$.,$Number of fraction of B$],[1,0\mathrm{.}45],[2,0\mathrm{.}50],[3,0\mathrm{.}65],[4,0\mathrm{.}55],[5,0\mathrm{.}40]]$