Question

Suppose the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs." That is, if P = profit, then P X  0.75 0.05.  Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for P.

Answer 1

Explanation:

Given that the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs."

i.e. Profit

= P(x) = 0.75 x - 0.05 where x is the no of dvds sold

E(x) =
`E(0.75x-0.05)\\= E(0.75x) -E(0.05)\\= 0.75E(x) -0.05`

(using linear transformation rules for mean)

VarP(x) =
`Var(0.75 x - 0.05)\\= Var(0.75x)\\= 0.75^2 Var(x)`

Hence std dev P(X) = 0.75 std dev (x)