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 ${\sigma }_X=1.29$.

(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 ${\mu }_{\mathrm{M}}$.

(c) Compute and interpret ${\sigma }_M$.

The money collected is the product of the cost for the ferry trip $\$5$and the number of cars $X:\$M=5X$The probabilities for $M$are the same as the probabilities for $\mathrm{X}\$$.

Create a probability histogram

The width of the bars has to be equal and the height has to be equal to probability.

Given

${\mu }_X=3.87$

${\sigma }_X=1.29$

The money collected is the product of the cost of the ferry trip $\$5$and the number of cars $X:M=5X$The probabilities for $M$are the same as the probabilities for .

Properties mean and standard deviation:

Then we obtain $f$or $M$

Given

${\mu }_X=3.87$

${\sigma }_X=1.29$

The money collected is the product of the cost for the ferry trip $\$5$and the number of cars localid="1649910262405" $X:\$M=5X$The probabilities for $M$are the same as the probabilities for $X$.

Properties mean and standard deviation: