The year-end bonuses of cash, stock and stock options (in thousands of US dollars) given to senior technical researchers in a leading chemical manufacturing company, each year over a ?ve-year period from 1990-1994, has a lognormal distribution with scale parameter α = 3 and shape parameter β = 0.5.
(i) Determine the probability that someone selected at random from this group received a bonus of $20, 000 or higher.
(ii) If a bonus of $100, 000 or higher is considered a "Jumbo" bonus, what percentage of senior technical researchers received such bonuses during this period?
(iii) If a bonus in the range $10, 000-$30, 000 is considered more typical, what percentage received this typical bonus?