In a study of the average heights of adults in a certain city, a random sample of 100 adults was taken. The sample mean height was found to be 165 cm with a standard deviation of 12 cm.
Using the Central Limit Theorem:
What is the standard error of the sample mean?
If we want to estimate the population mean height with 95% confidence, what would be the margin of error?
Based on the sample data, provide the 95% confidence interval for the population mean height.
(Note: Assume the z-value for 95% confidence is approximately 1.96)