Confident Interval

From a manufactory’s production line, there are two types of soda products: Apple and Cherry flavors. Your job is to randomly select samples from the each product line and monitor the quality of the products from data you have measured. You have used the same protocol of analysis for both products. In an initial analysis, 535 samples of Apple soda and 653 samples of Cherry soda samples were analyzed. The mean and standard deviation of the density from Apple soda was found to be 1.27 g/ml and 0.15 g/ml, respectively. The standard deviation of densities from Cherry soda was found to have the same value as from Apple soda, probably due to the same protocol of analysis.

You have measured the density of a random Cherry soda yesterday and found its value as 1.09 g/mL. Estimate the 95% confident interval of the mean for the entire population of Cherry soda from this single measurement.