Rodney partida is an American who is of Mexican ancestry. He was convicted of burglary with intent to commit rape. His conviction took place in hidalgo county, which is in texas on the border with mexico. Hildago county had 181,535 people eligible for jury duty, and 80% of them were Americans of Mexican ancestry. Among 870 people selected for grand jury duty 39% (339) were Americans of Mexican ancestry. Partida's conviction was later appealed on the basis of the large discrepancy between the 80% of Americans of Mexican ancestry eligible for grand jury duty and the fact that only 39% of such Americans were actually selected.

1. given that Americans of Mexican ancestry constitute 80 % of the population of those eligible for jury duty and given that partida was convicted by a jury of 12 people with only 58% (7 jurors) of them were Americans of Mexican ancestry. Discuss whether we can conclude that his jury was selected in a process that discriminates against Americans of Mexican ancestry (create a probability distribution to provide mathematical evidence for your conclusion)

2. given that Americans of Mexican ancestry constitute 80 % of the population, it is noted that during a period of 11 years, 870 people were selected for duty on a grand jury.

a) assuming that groups of 870 grand jurors are randomly selected, find the mean and standard deviation for the numbers of Mexican Americans

b) use the "rule of thumb" to find the minimum usual number and the maximum usual number of Mexican-americans. Based on those numbers, discuss whether we can conclude that the actual result of 339 mexican-americans is unusual. Does this suggest that the selection process discriminat4ed against Mexican-americans?