Question

The demand for Carolina Industries’ product varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company’s monthly demand: Unit Demand Probability 300 0.20 400 0.30 500 0.35 600 0.15 c. What are the variance and standard deviation for the number of units demanded?

Answer 1

Answer:

The variance is "9475" and standard deviation is "97.3396112".

Step-by-step explanation:

Let's all make the assumption that X seems to be the discrete uniformly distributed random indicating demand for units, and that f(x) has been the corresponding probability.

The expected value of the monthly demand will be:

⇒  $E(X)=\sum_{x} x\times f(x)$  

⇒            $=00\times 0.20+400\times 0.30+500\times 0.35+600\times 0.15$

⇒            $=445 \ units$

The variance will be:

⇒  $Var(X)=E(X^2)-{E(X)}^2$

⇒  $E(X^2)=\sum_{x} x^2\times f(x)$

                $=(300)^2\times 0.20+(400)^2\times 0.30+(500)^2\times 0.35+(600)^2\times 0.15$

                $=207500$

⇒  $Var(X)=207500 - (445)^2$

                  $=9475$

The standard deviation will be:

⇒  $X=\sqrt{var(X)}$

         $=97.3396112$