The proportion of time per day that all checkout counters in a supermarket are busy is a random variable Y with a denslt function given by y)-{cy (1-y), 0sys1, 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.) a-0 1572 (d) Find P(Y> + 20). (Round your answer to four decimal places.) o 0106

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