Ask Question
10 February, 21:55

A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the total of all rolls exceeds 400. approximate the probability that this will require more than 140 rolls.

+2
Answers (1)
  1. 11 February, 01:03
    0
    Let S = X1 + X2 + ... + X140

    Get E[X] and Var[X]

    E[X] = (6 + 1) / 2 = 7/2

    Var [X] = (6^2 - 1) / 12 = 35/12

    So E[S] = 140 (7/2) = 490 while Var [S] = 140 (35/12) = 1225/3

    Use the central limit theorem with continuity correction in finding the probability.

    Pr {S ≤ 400}

    Pr {S < 400.5 - 490 / √ (1225/3) }

    The answer should be 0.000004
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the total of all rolls exceeds 400. approximate ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers