We have 95 students in a class. Their abilities/eagerness are uniform randomly distributed on a scale...

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We have 95 students in a class. Their abilities/eagerness areuniform randomly distributed on a scale between 1 and 4; and at theend of the class they will be judged right and they will receive agrade corresponding to their ability/eagerness (corresponding totheir performance). What is the probability that the class averagewill be between 2.8 and 4? How would this number change (if itdoes) for 120 students?

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We are given the distribution for each student here asTherefore the mean and variance of this distribution is    See Answer
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