A student submits 7 assignments graded on the 0-100 scale. We assume that each assignment is an independent sample of his/her knowledge of the material and all scores are sampled from the same distribution. Let X₁,..., X7 denote the scores and 2 = 1 X; their average. Let p denote the unknown expected score, so that E [X₂] = p for all i. What is the maximal value z, such that the probability of observing Z≤z when p = 50 is at most 8 = 0.05?

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