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Q59Section C (Section C)59 of 60

Variance from a central limit approximation

Let X1,X2,…,X100X_1,X_2,…,X_{100} be i.i.d. random variables with E(X1)=0E(X_1)=0, E(X12)=σ2E(X_1^2)=\sigma^2, where σ>0\sigma>0. Let S=∑i=1100XiS=\sum_{i=1}^{100}X_i. If an approximate value of P(S≤30)P(S\le30) is 0.93320.9332, then σ2\sigma^2 equals __________________

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