Final answer:
The question involves calculating the probability that a candidate will be forecasted as an election winner based on sample voting results, applied to the context of population proportions and confidence intervals in statistics. Standard statistical methods, including hypothesis testing and Z-scores, would be utilized to find the probability if more details or assumptions are provided.
Step-by-step explanation:
The student is asking about the probability of a candidate being forecasted as the winner of an election based on certain sample result proportions within the framework of inferential statistics, specifically confidence intervals and population proportions. When a candidate has received 54% of the vote in a sample size of 100, and we want to determine the probability that this candidate is the true winner when her actual popular vote percentage is 50.13%, we need to consider the sampling distribution's standard error and employ a hypothesis test to calculate the probability (p-value) of observing a sample proportion at least as extreme as 54% if the true population proportion is indeed 50.13%.
The basic idea is that, under the null hypothesis that the true population proportion is 50.13%, the sample proportion of 54% might indicate a statistically significant difference, allowing us to forecast the candidate as the possible winner. However, the question is not fully answerable without more details about the expected variability in the voting population (standard deviation) or without making additional assumptions. In practice, this calculation would involve standard statistical techniques such as using the Z-score formula, where the Z-score indicates how many standard deviations a data point (like the sample proportion) is from the mean (the hypothesized population proportion).