Sample size is smaller than 30 We have learned that when sample size is less than 30, CLT is not applicable for the distribution of sample mean to be normally distributed. Therefore, we must construct a distribution table for sample mean when we want to use sample to infer population. Let a bag contains 5 balls numbered by 1, 2, 3,4, 5. Run a simple random sampling by picking up 3 balls at once. Answer the following questions: (Hint: construct a table for possible outcomes and the probability of possible outcomes.) A. Construct the table of the sample distribution of the sample mean (i.e., x=x1= x1+X2= x2+X3= x314? IIIIIIIIII Outcome b. Is the sample mean of (a) normal distributed? Is the center of the distribution of sample mean the same as the population? Is the Spread of the sample mean the same as the population? Explain your answers. (Hint: rst, calculating population mean and population variance. Then calculating sample mean and sample variance. Finally, compare two set of results from the rst step and the second step.)