In one case that made it all the way to the Supreme Court, a defense lawyer in Michigan challenged the process of selecting the jury pool in the trial of his accused client. Here are the facts: • About 7.28% of the citizens in the court’s jurisdiction were black.
• The jury pool had between 60 and 100 members, only 3 of whom were black.
Is it plausible that a jury pool with so few black citizens could be chosen just by chance?
For now, assume that the court carried out a proper random-selection process to obtain a jury pool with 100 members.
1. Let X = the number of black citizens in the jury pool. What distribution does the random variable X have? Justify your answer.

2. Find the mean and standard deviation of X. Interpret these values in context.

3. If a jury pool has 3 or fewer blacks, do we have convincing evidence that the court did not carry out the random selection process correctly? Compute P(X ≤ 3) and use this result to support your answer.

What if the jury pool had 60 members? Assume once again that the court carried out a proper random-selection process. Let Y = the number of black citizens in the jury pool.

4.Without doing any calculations, decide if P(Y ≤ 3) is greater than, equal to, or less than P(X ≤ 3). Justify your answer.

5. Using the logic of Question 4, explain why you do not have to consider jury pools with 61, 62, . . . , 99 members to render a verdict about whether or not the jury-selection process was carried out properly.
What is your verdict?