Example 5.10.1 Castaneda v. Partida. In Example 5.2.1 on page 250, 220 grand jurors were chosen from a population that is 79.1 percent Mexican-American, but only 100 grand jurors were Mexican-American. The expected value of a binomial random variable X with parameters 220 and 0.791is . This is much larger than the observed value of X = 100. Of course, such a discrepancy could occur by chance. After all, there is positive probability of for all . Since the court assumed that X had a binomial distribution with parameters , we should be interested in whether P is substantially less than the value 0.791, which represents impartial juror choice. For example, suppose that we define discrimination to mean that . We would like to compute the conditional probability of .