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 $\tau =\chi +\gamma$

Compute $\sigma \tau$assuming that $\chi$ and $\gamma$ are independent. Show your work.

Short answer

From the given information, the standard deviation is$1.14$

Step-by-step solution

Given Information

It is given in the question that,

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

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

$\tau =\chi +\gamma$

Explanation

The standard deviation of $\tau$can be calculated as:

localid="1649912163260" $$\begin{gathered} {\sigma }_T=\sqrt{(0.943{)}^2+(0.64{)}^2} \\ =\sqrt{1.2988} \\ =1.14 \end{gathered}$$