CALCULATIONS :-

i) Produce the linear portion DE of the graph further to meet Voltage axis.
DE meets voltage axis at 275 mV.
So cut-in voltage is 275 mV.

ii) The breakdown voltage is 4.1 Volts.

iii) Let us apply a signal (a.c voltage) at point in between B & C on linear portion of graph.
Then r_z = (delta)V_z / (delta)I_z
= (4.25 - 4.1) V / (50 - 5.5) micro A
= 0.15 V / 44.5 x 10^-6 A
= 3.37 k ohms.