Question

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Answer 1

Using the Central Limit Theorem, it is found that a larger sample size reduces the variability, that is, the experimental probabilities will be closer to the theoretical probabilities, which explains why the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times.

What does the Central Limit Theorem states?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard error $s = \sqrt{\frac{p(1 - p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$.

That is, the standard error is inverse proportional to the square root of the sample size, hence a larger sample size reduces the variability, that is, the experimental probabilities will be closer to the theoretical probabilities, which explains why the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times.

More can be learned about the Central Limit Theorem at brainly.com/question/16695444