ACTIVITY 7: Central Limit Theorem A. Consider the following scores of 5 students in Statistics. Student Statistics Score 67 61 90 78 1. Compute the mean of the population (#). (2 points) 2. Suppose sample size of 2 are drawn from this population, list all 10 possible samples and their corresponding means. (10 points) Samples Mean 3. Construct the sampling distribution of the sample means. Then compute for the mean of the sample means. (12points) Sample Mean (X) Probability P(X) X - P(X) 4. Compare the population mean and the mean of the sampling distribution. (1 point) B. Answer what is being asked. 1. The heights of the INHS SHS students are normally distributed with the mean of 65 inches and the standard deviation of 3 inches. If 50 samples consisting of 16 students each are drawn from the population, what would be the expected mean and standard deviation of the sampling distribution of the means? a. Identify the given information (2 points) b. Find the mean of the sampling distribution (2 points) c. Find the standard deviation of the sampling distribution (2 points) 2. Determine the standard error of the mean if the population has a mean of 150. Its standard deviation is 36 with the sampling size of sampling distribution equal to 16. a. Identify the given information (2 points) b. Find the standard error of the mean. (2 points)