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Using the formulas for the mean and standard deviation of a discrete random variable, calculate to 2 decimal places the mean and standard deviation for the population probability distribution of the table below. x P(x) 72 0.20 78 0.18 81 0.45 98 0.17 82.3 Click if you would like to Show Work for this question: Modify Show WorkThe following data give the ages (in years) of all six members of a family. 55 51 29 27 22 12 Let x denote the age of a member of this family. What is the probability P(r = 51)? Round your answer to three decimal places. P( =51) the absolute tolerance is +/-0.001 Click if you would like to Show Work for this question: Open Show WorkThe following data give the ages (in years) of all six members of a family. 56 50 29 26 21 13 List all possible samples of size five (without replacement) that can be selected from this population. Calculate the mean for each of these samples. Enter the exact answers. For a sample 56, 50, 29, 26, 21, mean = For a sample 56, 50, 29, 26, 13, mean = For a sample 56, 50, 29, 21, 13, mean = For a sample 56, 50, 26, 21, 13, mean = For a sample 56, 29, 26, 21, 13, mean = For a sample 50, 29, 26, 21, 13, mean = Write the sampling distribution of &. Find P (x =27.8). Round your answer to three decimal places. P (1 =27.8) =Consider a large population with & = 80 and o = 11. Assuming N