Example #3 A study by the National Association of Realtors reports that second-home sales accounted for more than a third of residential real estate transactions in 2004. According to the report, the average age of a person buying a second home as a vacation was 55 years. A real estate agent wants to estimate the average age of those buying vacation homes in her area. She randomly selects 15 of her clients who purchased a vacation home and o brains the data below. Assume that () = 4.7 47. 351 52 51 55 49 51 54 51 47 37141 47 40 48 a) What is the point estimate of the population mean age of the real estate agent's clients who purchased a vacation home? b) Assume that the data was taken from a population that's normally distributed. Construct a 99% confidence interval for the mean age for all the real estate agent's clients who purchased a vacation home. Interpret this result