Section 6 - 6: Central Limit Theorem 1. Compute all the possible sample means of of { 3, 5, 7 ) taken two at a time (with replacement). Complete the frequency tables for the distributions x and X . Calculate the mean and standard deviation for each distribution. 7 = * = + No + 2 $1 = 51 = + + $1 = 2 2 3 + Is = Is = N + 2 NA = + x: A + 2 2 population of 3 values Ts = Is = 2 To = the calculation of the sample means emit for every possible sample of 3 values the distribution of all taken two at a time with replacement you bas wo sample means if n = 2 Complete the tables below and use a calculator to compute the following: X f(x) f (7 ) Mean , = 5 Standard Deviation of = Mean MT = Standard Deviation Standard V2 Deviation of =2. Compute all the possible sample means of of { 2, 4, 10 } taken two at a time (with replacement). Complete the frequency tables for the distributions x and X . Calculate the mean and standard deviation for each distribution. $1 = + + 2 2 $1 = + + 2 2 + + 4 Tg = 2 2 10 + + x: A 2 population of 3 values Is = To = the calculation of the sample means for every possible sample of 3 values x the distribution of all taken two at a time with replacement sample means if n = 2 Complete the tables below and use a calculator to compute the following: f(x) f(F ) 2 Mean M. = Standard 10 Deviation of = Mean M- = Standard Standard Deviation O -= Deviation of = V2This section refers to X , the distribution of all the possible sample means of a population of size n. This is a distribution of the random variable 2 18 8. What can you say about the value of the standard deviation of a population of, compared to the value of the standard deviation of the distribution of all the possible sample means of for that same population? 9. What can you say about the value of the mean of the distribution of all the possible sample means up as the sample size (n) increases? 10. What can you say about the value of the standard deviation of the distribution of all the possible sample means or as the sample size (n) increases