Answer:
(a) $2000
(b) $94.9
Step-by-step explanation:
The expected $ value of signing 100 deals with probability of 0.1 each is
E(X) = 100*0.1 + 100*0.1 + 100*0.1 + ... + 100*0.1 = 100(100*0.1) = $1000
Along with the fixed amount of $1000, the total next month salary is $2000
As for the standard deviation we can apply the following formula
[tex]\sigma = E(X^2) - E(X)^2[/tex]
[tex]\sigma = \sqrt{0.1*(100 - \mu)^2 + 0.1*(100 - \mu)^2 + ... + 0.1*(100 -\mu)^2}[/tex]
[tex]\sigma = \sqrt{0.1*100*(100 - 1000)^2}[/tex]
[tex]\sigma = \sqrt{10*900^2} = \sqrt{9000} = 94.9[/tex]
