Answer to Question #70363 in Statistics and Probability for Jester

Question

Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The p.d.f that characterizes the proportion Y that make a profit is given by: ky^4(1-y)^3 and 0 elsewhere.
A. What is the value of k that renders the above a valid density function?
B.Find the probability that at most 50% of the firms make a profit in the first year.
C. Find the probability that at least 80% of the firms make a profit in the first year.