_ n __ Greg plays a game when he exercises. He choose a marble from a bag of three marbles: one Is blue, one is green, and one -;.- is red. Based on the marble he chooses, he completes a certain number of push-ups, as shown below. ._ - ' Marble Number of push-ups - @ lea\" Consider choosing a marble like sampling from a population. (The population mean of the number of push-ups ls [1-100 and the populadon standard deviation is cal-0.32.) (a) Suppose a sample of size 2 Is randomly selected from the population, with replacement, as follows. One marble ls randomly chosen, the number of push-ups is completed, and the marble is put back into the bag. Then for a second time a marble ls randomly chosen and the number of pushups is completed. There are 9 possible samples. The numbers of push-ups for several of the possible samples have been listed in the table below. Enter the numbers of push-ups for the remaining possible samples. When you are done, select 'Compute". In the Sample mean, x' column, you will then see the sample mean of the numbers of push-ups for each sample, along with the mean and standard deviation of all the oolumn's values. Numbers _ Index Sample of push- Sample mean, .1: up: II- um Use the table from part (a) to find P; (the mean of the sampling distribution of the sample mean) and G;(tl1e standard deviation of the sampling distribution of the sample mean). Write your answers to two decimal places. (C) Graph the frequenw histograms for the population distribution and the sampling distribution of the sample mean. Population distribution Sampling distribution of the sample mean