5.97 Short term versus long run According to countrymeters.

info, the American population in 2016 consisted of 49.4%

males and 50.6% females. To illustrate how short-term aberrations do not affect the long run, suppose that you select 10 Americans and you get 10 males.

a. Find the cumulative proportion of males, including the first 10 selections, if (i) you select 100 more Americans and you get 49 males; (ii) you select an additional 1000 Americans and you get 494 males; and (iii) you select an additional 10,000 Americans after those 10, you get 4940 males.

b. What number does the cumulative proportion tend to as n increases?