Answer
a) $4\;\rm m/s$
b) $4.6\;\rm m/s$
c) $4.94\;\rm m/s$
Work Step by Step
a) As we see in the given figure, the most probable speed is at the highest column.
So
$$v_{most}=\color{red}{\bf 4}\;\rm m/s$$
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b) We have about $N$ particles and the average speed of them is given by
$$v_{avg}=\dfrac{v_1+v_2+..+v_N}{N}$$
Hence,
$$v_{avg}=\dfrac{2(2)+4(4)+3(6)+(8)}{2+4+3+1}=\color{red}{\bf 4.6}\;\rm m/s$$
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c) we know that the rms speed is given by
$$v_{\rm rms}=\sqrt{\dfrac{v_1^2+v_2^2+...+v_N^2}{N}}$$
Hence,
$$v_{\rm rms}=\sqrt{\dfrac{2(2)^2+4(4)^2+3(6)^2+(8)^2}{2+4+3+1}}=\color{red}{\bf 4.94}\;\rm m/s$$
