The proportion of time per day that all checkout counters in a supermarket are busy is a random variable Y with a density function given by Scy³(1 - y)4, osys1, f(y) elsewhere. (a) Find the value of c...

Extracted text: The proportion of time per day that all checkout counters in a supermarket are busy is a random variable Y with a density function given by Scy³(1 - y)4, osys1, f(y) elsewhere. (a) Find the value of c that makes f(y) a probability density function. C-280 (b) Find E(Y). (Use what you have learned about the beta-type distribution.) E(Y) 0.4444 x (c) Calculate the standard deviation of Y. (Round your answer to four decimal places,) o - 0 1572 (d) Find P(Y>+ 20). (Round your onswer to four decimal places.) 0 0196