Question

a small software company will bid on a major contract. it anticipates a profit of $35,000 if it gets it but there is only a 10% chance of that happening.
1. find the standard deviation for the profit

Answer 1

Let X be a random variable denoting the profit of the company( in dollar).

It is given, that the company gains a profit of $35000 if it gets a major contract with probability 0.1. Otherwise we assume the profit is 0.

Thus, X takes value 35000 with probability 0.1 and takes value 0 with probability (1-0.1) =0.9.

1)

Thus, E(X) ==(35000*0.1) +(0*0.9) =3500.

Again, E(X²) ==(35000²*0.1) +(0*0.9) =122500000

Thus, the variance of profit, i.e., X is,

var(X) =E(X²) -[E(X)]²=122500000-3500²=110250000.

Therefore, the standard deviation of the profit is, √110250000=10500.

Thus the standard deviation of the profit is $10500.