The following data are for a liquid chromatographic column
$$\begin{array}{ll}
\hline \text { Length of packing } & 24.7 \mathrm{cm} \\
\text { Flow rate } & 0.313 \mathrm{mL} / \mathrm{min} \\
V_{\mathrm{M}} & 1.37 \mathrm{mL} \\
V_{\mathrm{s}} & 0.164 \mathrm{mL} \\
\hline
\end{array}$$
A chromatogram of a mixture of species $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D}$ provided the following data:
$$\begin{array}{lcc}
& \begin{array}{c}
\text { Retention } \\
\text { Time, min }
\end{array} & \begin{array}{c}
\text { Width of Peak } \\
\text { Base }(W), \min
\end{array} \\
\hline \text { Nonretained } & 3.1 & - \\
\text { A } & 6.2 & 0.49 \\
\text { B } & 13.3 & 1.07 \\
\text { C } & 15.7 & 1.32 \\
\text { D } & 21.6 & 1.72
\end{array}$$
Calculate
(a) the number of plates from each peak.
(b) the mean and the standard deviation for $N$
(c) the plate height for the column.