A more thorough explanation:

Statistical-decision theory is a method used to determine if a group of potential jurors was selected from a fair cross-section of the community. This is done by calculating the probabilities of selecting a certain number of jurors from a particular group to analyze whether it is statistically probable that the jury pool was selected by mere chance.

For example, if a jury pool of 100 people is made up of 80 men and 20 women, statistical-decision theory can be used to determine if this is a fair representation of the community. If the community is made up of 50% men and 50% women, then the jury pool is not a fair cross-section and may be biased.

However, it is important to note that potential jurors are not selected by mere chance. They are disqualified for various legitimate reasons, such as not being a citizen or having a criminal record. Therefore, statistical-decision theory has been criticized for not taking these factors into account.

Overall, statistical-decision theory is a useful tool for analyzing the fairness of a jury pool, but it should be used in conjunction with other methods to ensure a truly representative cross-section of the community.