Chapter 7, Problem 37SE

Jury Selection (Example 6) Juries should have the same racial distribution as the surrounding communities. According to the U.S. Census, about $18\%$ of residents in Minneapolis, Minnesota, are African American. Suppose a local court randomly selects 100 adult citizens of Minneapolis to participate in the jury pool.

Use the Central Limit Theorem (and the Empirical Rule) to find the approximate probability that the proportion of available African American jurors is more than two standard errors from the population value of 0.18.

The conditions for using the Central Limit Theorem are satisfied because the sample is random; the population is more than 10 times 1000; n times p is 18, and n times (1 minus p) is 82, and both are more than 10.