Answer:
Step-by-step explanation:
Let's start writing the random variables :
X1 : ''The number of 27 containers shipped during a given week''
X2 : ''The number of 125 containers shipped during a given week''
X3 : ''The number of 512 containers shipped during a given week''
We assume that X1, X2 and X3 are independent (data from the exercise).
The random variable T : ''Total volume shipped during a given week'' has the following equation :
We want to calculate E(T) and (σ^2)(T).
In the following equations : (σ^2)(X) = V(X)
The expected value operator works as a linear operator.
Then, we calculate E(T) as the following :
We use the information from the exercise ⇒
For the variance :
If X1, X2, X3, ... , Xn are independent random variables, then ⇒
Applying this to the exercise :
We square the standard deviations to obtain the variance of X1,X2 and X3