The following table shows a partial probability distribution for the Pitt & Gorilla Toy Company's projected profits (in thousands of dollars) for the coming year, 2024 (the negative value denotes a loss):

Profit (X) Probability P(x)

--------------------------------------------

-20 0.15

-10 0.10

0 0.20

10 0.25

20 0.20

30 ?

---------------------------------------------

1. Find the missing value of P (30). What is your interpretation of this value?

2. What is the probability that Pitt & Gorilla Toy Company will be profitable?

3. What is the expected profit for this company in 2024?

4. What is the variance of the projected profit for this company in 2024?