Science:Math Exam Resources/Courses/MATH102/December 2012/Question B 04/Solution 1

Since we have three possible outcomes here (selling 1, 2, or 3 cars), we will use a formula for expected value that looks like this:

$\displaystyle E[X]=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}$

Where $x_{i}$ is the money earned (or value) of selling i cars in a month and $p_{i}$ is the corresponding probability of selling i cars. Plugging in the appropriate probabilities and amount earned per car (plus the $1000 dollar bonus if 3 cars are sold!), we get:

$\displaystyle E[X]=2000*.7+4000*.2+7000*.1$

Simplifying gives:

$\displaystyle E[X]=2900$

So the sales person's expected monthly income is $2,900.