Final answer:
The content in question relates to the central limit theorem for sums and calculating the expected value and standard deviation of a sum's sampling distribution. The z-score for the sum of random variables can be calculated using a specific formula provided by the central limit theorem.
Step-by-step explanation:
The initial question about the z-transform and region of convergence (ROC) of a sequence seems to be out of context with the subsequent information provided. The provided detail pertains to probability, the normal distribution, and the central limit theorem for sums, rather than to z-transforms. To address the related content accurately, consider the central limit theorem which states that the sum of a large number of independent, identically distributed random variables will be approximately normally distributed. For sums, the expected value and standard deviation of their sampling distribution can be calculated using the formulae provided in the central limit theorem section.
The z-score for the sum of random variables (EX) can be found by the formula: Z = (ΣX – (n)(μX)) / ((√n)(σX)), where ΣX represents the sum of the random variables, n is the sample size, μX is the mean, and σX is the standard deviation of the original distribution.