The monthly sales at a computer store have a mean of 25000 a

The monthly sales at a computer store have a mean of $25,000 and standard deviation of $4,000 . Profits are 30 % of the sales less fixed costs of $6,000 . Find the mean and standard deviation of monthly profit .

Solution

Sales : S, E(S) = 25000 $

Sales : S , SD(S) = 4000 $, V(S) = 4000^2

Profit function = 30% S - 6000

P = 0.3S - 6000

E(P) = E(0.3S - 6000)

E(P) = 0.3 E(S) - 6000

E(P) = 0.3 * 25000 - 6000

E(P) = 1500 MEAN PROFIT

V(P) = V(0.3S - 6000)

V(P) = 0.3^2 V(S) - 0

V(P) = 0.09 * 4000^2

V(P) = 1440000

SD(P) = SQRT(V(P))

SD(P) = 1200 $