To improve their incentive compensation program, the manager has been

conducting

a study involving random surveys of employees in four departments,

Personal Accounts $($A$),$ Small Business Accounts $($B$),$ Corporate Accounts

$($C$),$ and Premium Banking $($D$).$ Each employee can receive a

performance rating from $1$ to $5.$ The following table presents the survey

results.

Performance ranking $($ X $)$

E$($ X$)$ Var$($ X$)$

x $12345$

P$($ X$=$x$)$ P$($ X$=1)$ P$($ X$=2)$ P$($ X$=3)$ P$($ X$=4)$ P$($ X$=5)$

A $0\mathrm{.}20\mathrm{.}20\mathrm{.}20\mathrm{.}20\mathrm{.}232\mathrm{.}00$

B $0\mathrm{.}50\mathrm{.}20\mathrm{.}20\mathrm{.}050\mathrm{.}05$

$1\mathrm{.}9$

$51\mathrm{.}35$

C

$0\mathrm{.}40\mathrm{.}30$