Please provide detailed solution:

The following table is the probability distribution for the MRA Company's projected profits (X = profit in 1,000s) for

the first year of operation. Negative value denotes loss.

X P(X)

-100 0.1

0 0.2

50 0.3

100 0.25

150 0.1

200 0.05

a. What is the probability that the project will be profitable in the first year of operation?

b. What is the probability that the project will have at least $100,000 profit in the first year of operation?

c. What is the probability that the project will be profitable and with less than $150,000 profit in the first year

of operation?

d. What is the expected profit in the first year of operation?

e. What is the standard deviation of the distribution?