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(4). A fair six-sided die is repeatedly rolled until the total sum of all rolls exceeds 300. Use the Central Limit Theorem to approximate the probability that at least 80 rolls are necessary. (Hint: Let Xi be the outcome of the ith roll. You can use the fact that X1, X2,... are iid random variables with E[Xi] = 7/2 and Var(Xi) = 35/12. Consider X = sum_{i=1}^{79} Xi. Then P(X <= 300) is the same as the probability that at least 80 rolls are necessary.)

          (4). A fair six-sided die is repeatedly rolled until the total sum of all rolls exceeds 300. Use the Central Limit Theorem to approximate the probability that at least 80 rolls are necessary.

(Hint: Let Xi be the outcome of the ith roll. You can use the fact that X1, X2,... are iid random variables with E[Xi] = 7/2 and Var(Xi) = 35/12. Consider X = sum_{i=1}^{79} Xi. Then P(X <= 300) is the same as the probability that at least 80 rolls are necessary.)

(4). A fair six-sided die is repeatedly rolled until the total sum of all rolls exceeds 300. Use the Central Limit Theorem to approximate the probability that at least 80 rolls are necessary.

(Hint: Let Xi be the outcome of the ith roll. You can use the fact that X1, X2,... are iid random variables with E[Xi] = 7/2 and Var(Xi) = 35/12. Consider X = sumi=1^79 Xi. Then P(X <= 300) is the same as the probability that at least 80 rolls are necessary.)

Added by Ernest K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Lucas Finney

11/27/2022

Step 1

79 \), \( \mu = 3.5 \), \( \sigma = \sqrt{35/12} \), and \( n = 79 \). Substitute the values: \( z = \frac{300.79 - 3.5}{\sqrt{35/12}/\sqrt{79}} \) \( z = \frac{297.29}{\sqrt{35/12}/\sqrt{79}} \) \( z = \frac{297.29}{\sqrt{35/12}/\sqrt{79}} \) \( z = Show more…

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A fair six-sided die is repeatedly rolled until the total sum of all rolls exceeds 300. Use the Central Limit Theorem to approximate the probability that at least 80 rolls are necessary. (Hint: Let Xi be the outcome of the ith roll. You can use the fact that X1, X2,... are iid random variables with E[Xi] = 7/2 and Var(Xi) = 35/12. Consider X = sum_{i=1}^{79} Xi. Then P(X <= 300) is the same as the probability that at least 80 rolls are necessary.)