Question: Historical data indicates that the starting salary for a new MBA graduate in a leading management consulting firm can be modelled as a normal distribution with mean $100,000 and standard deviation $20,000. Second year salaries increase by 20%. The bonus each year, for the first and following years, can be modelled as a normal distribution with mean $25,000 and standard deviation $5000. Assume that the bonus is independent of the initial salary, and also independent from the annual salary increase. If annual compensation equals salary plus bonus, answer the following questions

a) What is the expected annual compensation for a new hire?

b) What is the standard deviation of the annual compensation for a new hire?

c) What is the expected annual compensation after completing a year in the firm?

What is the standard deviation of the annual compensation after completing a year

in the firm?