Question

k

Answer 1

so
P = .40*S - 12,000

Answer 2

we have a new random variable

Answer 3

we can use our rules about mean and variance

Answer 4

here is a useful formula
E[aX + b] = aE[X] + b

Answer 5

and
Var[aX+b] = a^2 Var[X]

Answer 6

or
Stdev(aX + b) = |a|Stdev(X)

Answer 7

we want
E[Profit]
= E [ .40*S - 12,000 ]
use our rule that gives us
.40 * E(S) + -12,000

Answer 8

so teh mean of the profit is .40 * 50,000 - 12000

Answer 9

yes

Answer 10

now for standard deviation
Stdev(aX + b) = |a|Stdev(X)

stdev ( .40 * S + -12,000 ) = |.40| * stdev ( S )