about real life implications of finding mean and the variance of the sampling distribution of the sample means and about central limit theorem

FINDING THE MEAN AND VARIANCE OF THE SAMPLING DISTRIBUTION OF THE SAMPLE MEANS Give the real life interpretation and implications of the following problems or situation: 1. The following table gives the sum of tutorial rate of six teachers in Central Luzon per month. Suppose that random samples of size 4 are taken from this population of six teachers, do the following tasks. (u don't need to answer the problem just give the real life interpretation about this problem) Teacher Tutorial Rate (in thousand pesos) X A 8 12 C 16 D 20 E 24 F 28 1) Solve for the mean of the population . 2) Solve for the mean of the sampling distribution of the sample means pix. 3) Compare p and pix . 4) Solve for the variance (o 2 ) and the standard deviation (o) of the population. 5) Solve the variance (o 2 x ) and the standard deviation (ox ) of the sampling distribution of the sample means pix . 6) Compare o and ox 2. Situation: After considering the first example on the previous part of this module, Harvey has some questions and difficulties in solving the mean and the variance of the sampling distribution of the sample means. Help Harvey in acquiring desired skills by doing the given activity below. It's all about computing the mean and the variance of the sampling distribution of sample means. CENTRAL LIMIT THEOREM 1. Do we always add or subtract from 0.50? Explain. 2. When do we add the corresponding area of the z-score to 0.50? 3. When do we add the two corresponding areas of the z-score