An RTD analysis was carried out on a liquid$-$phase reactor. Analyze the following data.

$\backslash$table$[[t(s),0,150,175,200,225,240,250],[c(m\frac{g}{m^3}),0,0,1,3,7\mathrm{.}4,9\mathrm{.}4,9\mathrm{.}7],[t(s),275,300,325,350,375,400,450],[c(m\frac{g}{m^3}),8\mathrm{.}2,5\mathrm{.}0,2\mathrm{.}5,1\mathrm{.}2,0\mathrm{.}5,0\mathrm{.}2,0]]$

a$.$ Plot the $E(t)$ curve for these data.

b$.$ Estimate $F(t)$ and plot the $F(t)$ curve for these data.

c$.$ What fraction of the materlal spends between $250$ and $300$ seconds in the reactor?

d$.$ What fractlon of the material spends less than $240$ seconds in the reactor?

e$.$ What is the mean residence time?

f$.$ What is the varlance ${}^2?$