20.21 Household size. The Census Bureau gives this distribution for the number of people in American households in 2016: Family size: 1 2 3 4 5 6 7 Proportion: 0.28 0.35 0.15 0.13 0.06 0.02 0.01 (Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7.) a. This is also the probability distribution for the size of a randomly chosen household. The expected value of this distribution is the average number of people in a household. What is this expected value? b. Suppose you take a random sample of 1000 American households. About how many of these households will be of size 2? Sizes 3 to 7? c. Based on your calculations in part (b), how many people are represented in your sample of 1000 households? (Hint: The number of individuals in your sample who live in households of size 7 is 7 times the number of households of size 7. Repeat this reasoning to determine the number of individuals in households of sizes 2 to 6. Add the results to get the total number of people represented in your sample.)