2:59 4 .I "3' Cl 5. People 65 years and older are the fastest growing segment of the US population, and constituted 13% of the population in 2010, according the Census (17.7% in 2020). Figure 1 shows sample proportions from two sampling distributions of the proportion 65 years and older in the US in 2010: One shows samples of size 100, and the other shows samples of size 1000. Figure 1. Sampling distributions for n = 100 and n = 1000 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 Proportion Age 65+ (n=100) 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 Proportion Age 65+ (n=1000) a. What is the center of both distributions? b. What is the approximate minimum and maximum of each distribution? 0. Give a rough estimate of the standard error in each case. (1. Suppose you take one more sample in each case. Would a sample proportion of 0.16 (that is, 16% senior citizens in the sample) be surprising to see from a sample of size 100'? Would it be surprising from a sample of size 1000