Final answer:
To calculate the 95% confidence interval for the population mean with a sample mean of 12.82, sample standard deviation of 2.27, and sample size of 137, you need to apply the confidence interval formula and use the corresponding z-score for the 95% confidence level.
Step-by-step explanation:
To calculate a 95% confidence interval for the population mean, given a sample size (N), sample mean (x), and sample standard deviation (s), you can use the following formula:
CI = x ± (z * (s / √N))
Where CI is the confidence interval, x is the sample mean, z is the z-score corresponding to the confidence level (for 95%, z is approximately 1.96), s is the sample standard deviation, and N is the sample size.
In the question provided, we have N = 137, x = 12.82, and s = 2.27. Plugging in the values, we get:
CI = 12.82 ± (1.96 * (2.27 / √137))
After calculating the margin of error, add and subtract it from the sample mean to find the confidence interval.
confidence interval, population mean, and sample standard deviation are the key concepts for solving this problem.