Question

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

Define$D=X-Y$

Find and interpret $\mu D$.

Short answer

From the given information, it is expected that$0.4$ more of the cars would be sold out than leasing.

Step-by-step solution

Given Information

It is given in the question that,

$\mu \chi =1.1,\sigma \chi =0.943$

$\mu \gamma =0.7,\sigma \gamma =0.64$

$D=\chi -\gamma$

Step 2: Explanation

The mean can be calculated as :

$$\begin{gathered} \mu D=\mu \chi -\mu \gamma \\ =1.1-0.7 \\ =0.4 \end{gathered}$$