You roll a​ die, winning nothing if the number of spots is odd​, ​$5 for a 2 or a 4​, and ​$20 for a 6. ​a) Find the expected value and standard deviation of your prospective winnings. ​b) You play five times. Find the mean and standard deviation of your total winnings. ​c) You play 50 times. What is the probability that you win at least ​$270​?

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TeX rendering has been iffy at best on this site for the past few days, at least in my experience. I've attached a solution below.

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