Get on the boat! A small ferry runs every half hour from one side of a large river to

QUESTION:

A small ferry runs every half hour from one side of a large river to the other. The number of cars X on a randomly chosen ferry trip has the probability distribution shown below. You can check that \(\mu_{X}=3.87\) and \(\sigma_{X}=1.29\).

\(\begin{array}{lcccccc} \hline \text { Cars: } & 0 & 1 & 2 & 3 & 4 & 5 \\ \text { Probability: } & 0.02 & 0.05 & 0.08 & 0.16 & 0.27 & 0.42 \\ \hline \end{array}\)

(a) The cost for the ferry trip is $5. Make a graph of the probability distribution for the random variable M = money collected on a randomly selected ferry trip. Describe its shape.

(b) Find and interpret \(\mu_{M}\).

(c) Find and interpret \(\sigma_{\mathrm{M}}\).