An industrial training company that offers week-long courses to corporations has three instructors on its permanent staff. The company receives requests for this courses from its many corporate clients. The course fee charged by the training company is $20,000 per course. The company also has a pool of qualified instructors in China that it can draw upon whenever demand for their courses exceeds their supply of permanent instructors. Under a standardized arrangement, an instructor in the pool receives 55% of the course fee whenever he/she teaches a course. The weekly demand for courses obeys the probability distribution given in the following:

Number of courses | Probability

0 0.05

1 0.15

2 0.25

3 0.25

4 0.15

5 0.10

6 0.05

Please show step by step workings.

Question 1a. What is the probability distribution of the company's weekly revenue after deducting payments to pool instructors?

Question 1b. Calculate the mean and standard deviation of the company's weekly revenue after deducting payments to pool instructors.

Question 1c. Adding more instructors to the permanent staff involves an incremental cost of $2,500 per instructor per week. If you are the boss of the company, how many additional permanent instructor(s) should you hire?