Y$(7$ points$)$ Suppose that Red Itchy Toes Syndrome $($RITS$),$ a variant of Blue Itchy Toes Syndrome, begins spreading through an elementary school. On the eighth day of the disease, the number of students in various stages of illness are as shown:

Stage

Day $8$

Day $9$

H

Healthy

$90$

$1$

Infected

$26$

$2$

Infected

$22$

$3$

Infected & Contagious

$9$

$4$

Infected & Contagious

$11$

$5$

Sick & Contagious

$5$

$6$

Sick & Contagious

$7$

$7$

Sick & Contagious

$4$

$8$

Sick & Contagious

$4$

R

Recovered

$3$