Question

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let $X$= the number of cars sold and $Y$= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of $X$and $Y$are as follows:

Define $T=X+Y$.

Find and interpret $\mu T$.

Short answer

From the given information, It is expected that $1.8$of the cars would be sold or leased out in the first hour of business.

Step-by-step solution

Given Information

It is given in the question that,

$\mu X=1.1\sigma X=0.943$

$\mu Y=0.7\sigma Y=0.64$

$\tau =\chi +\gamma$

Explanation

The mean of T can be calculated as:

$$\begin{gathered} \mu \tau =\mu \chi +\mu \gamma \\ =1.1+0.7 \\ =1.8 \end{gathered}$$