Final answer:
About 95% of the 95% confidence intervals would be expected to contain the population mean of 50, reflecting the underlying theoretical properties of confidence intervals.
Step-by-step explanation:
To find the proportion of the 95% confidence intervals that contained the population mean of 50, it is important to understand that under normal circumstances, if we calculated many 95% confidence intervals from different samples of the population, about 95% of these intervals would contain the population mean. If we had generated 100 confidence intervals, we would expect that approximately 95 of them would contain the population mean of 50.
This is based on the property of a 95% confidence interval which aims to capture the population mean 95% of the time. Therefore, if in practice a different proportion was observed, it would indicate a deviation from the theoretical expectation, possibly due to sample size or variability.