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What is the approximate probability that a die with six sides that are each equally likely to appear will require more than 140 rolls for the total of all rolls to exceed 400?
Wiki User
∙ 10y ago
More than 140 rolls will be required if and only if the sum of the first 140 rolls does not exceed 400
Let S = X1 + X2 + ... + X140 where Xi is the number obtained in the ith rollNote E[X] = 7/2, Var[X] = 35/12
So E[S] = 140(7/2) = 490, Var[S] = 140(35/12) = 1225/3
By Central Limit Theorem, (with continuity correction)
Pr{S ≤ 400}
≈ Pr{Z < (400.5 - 490)/√(1225/3)}
≈ 4.731327 * 10^(-6)
Wiki User
∙ 10y ago
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