A die is rolled 24 times. Use the Central Limit Theorem to estimate the probability that the sum is greater than 84.

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: C

On each roll, the expected number is

[[math]] 1/6 \sum_{i=1}^6 i = 3.5 [[/math]]

Hence the expected sum for 24 rolls is 84. By the central limit theorem, the probability that 24 rolls exceed 84 is 1/2.