Salaries differ greatly between faculty members at public universities in the united states. full professors (who have tenure and do research) earn an average of $125,572 per year with a standard deviation of $18,328. associate professors (who are working towards tenure and do research) earn an average of $90,101 per year with a standard deviation of $12,741. lecturers (whose primary responsibility is teaching and do not earn tenure) earn an average of $59,707 per year with a standard deviation of $7,386. assume all three populations are normally distributed.
a. what is the probability that a randomly selected full professor makes less than $100,000 per year?