I have a balanced 5-sided die. (That is, the sides are numbered 1,2,3,4,5.) (a) 1 roll...

 

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I have a balanced 5-sided die. (That is, the sides are numbered 1,2,3,4,5.) (a) 1 roll it once, and if the roll is a k, I receive k dollars. (For instance, if I roll a 3, I get $9.) How much do I expect to receive? (b) I roll it 15 times. Find the probability that I will roll exactly 5 threes. (Do not approximate.) (c) I roll it 625 times. Use a normal approximation to estimate the probability that I will roll at least 108 but fewer than 127 threes. I have a balanced 5-sided die. (That is, the sides are numbered 1,2,3,4,5.) (a) 1 roll it once, and if the roll is a k, I receive k dollars. (For instance, if I roll a 3, I get $9.) How much do I expect to receive? (b) I roll it 15 times. Find the probability that I will roll exactly 5 threes. (Do not approximate.) (c) I roll it 625 times. Use a normal approximation to estimate the probability that I will roll at least 108 but fewer than 127 threes.

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