## Calculate

The text discusses confidence intervals and their relationship to the normal distribution and Z-scores. It explains how a confidence interval is used to estimate the population mean by using the sample mean and a certain level of confidence, such as 90% or 95%. The confidence interval is calculated by using a Z-score, which is different depending on the desired level of confidence. The purpose of a confidence interval is to give a range of values within which the true population mean is likely to fall. The text also mentions that the wider the interval, the more confident we can be that it contains the population mean. Finally, it notes that if multiple confidence intervals are constructed using different samples, we would expect a certain percentage of them to include the true population mean.

It seems that the results from the search don't directly provide the specific calculations for the confidence interval based on the given data. However, I can directly compute the 90% confidence interval for the mean age for all the real estate agent's clients who purchased investment property using the provided sample data and the given population standard deviation.

Let me calculate the confidence interval based on the given information.

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