The binomial probability distribution for the number of Mexican-American jurors among 12 people in a jury
5-2 page 203 number 13 (link to answer)
Assume that jurors are randomly selected from a population in which 80% of the eligible people are Mexican-American.
= number of Mexican-American jurors
Use the table to the right to answer the questions.
a. Find the probability of a jury having exactly 5 Mexican-Americans among 12 jurors.
0.3% is the probability that exactly 5 of 12 jurors are Mexican-Americans.
b. Find the probability of a jury having 5 or fewer Mexican-Americans among 12 jurors.
0.003 + 0.001 = 0.4%
0.4% is the probability that 5 or fewer jurors are Mexican-Americans.
c. Is "exactly 5" or "5 or fewer" more useful for determining whether or not 5 Mexican-Americans jurors among 12 is unusually low?
We wish to know if the particular case of 5 Mexican-Americans jurors is unusual. By choosing a range of numbers (0 to 5 in part b) that is unusual, it is extremely easy to decide whether any particular number of Mexican-Americans jurors is unusual.
d. Does the fact that a particular jury exists which contains 5 Mexican-Americans jurors out of 12 support (or not) the claim that the selection process discriminates against Mexican-Americans.
Since the probability of 5 or fewer Mexican-Americans jurors among 12 is smaller than 5%, we can conclude that any jury containing 5 or fewer Mexican-Americans jurors among 12 is unusual, hence unlikely to occur by chance. Thus, the statistical analysis supports the claim that the selection process discriminates against Mexican-Americans.