Question 8.2.13: Suppose one hundred numbers X1, X2, ..., X100 are chosen ind......
Suppose one hundred numbers X1, X2, …, X100 are chosen independently at random from [0, 20]. Let S = X1 + X2 + ··· + X100 be the sum, A = S/100 the average, and S∗ =(S −1000)/(10/\sqrt{3}) the standardized sum. Find lower bounds for the probabilities
(a) P(|S − 1000|≤ 100).
(b) P(|A − 10|≤ 1).
(c) P(|S∗|≤\sqrt{3}).
(a) 2/3
(b) 2/3
(c) 2/3
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