Question

A survey estimates that 14.7% of Americans live below the poverty line, 20.1% 5peak a language other than English (foreign language) at home, and 4.6% fall into both categories. (a) Are living below the poverty line and speaking a foreign language at home disjoint? Yes, because no one is both living below the poverty line and speaking a language other than English at home. No, because there are people living below the poverty line and speaking a language other than English at home. (b) Draw a Venn diagram summarizing the variables and their associated probabilities. (Enter your answers to three decimal places.) (c) What percent of Americans live below the poverty line and only speak English at home? (Enter your answer to one decimal place.) % (d) What percent of Americans live below the poverty line or speak a foreign language at home? (Enter your answer to one decimal place.) % (e) What percent of Americans live above the poverty line and only speak English at home? (Enter your answer to one decimal place.) % (c) What percent of Americans live below the poverty line and only speak English at home? (Enter your answer to one decimal place.) % (d) What percent of Americans live below the poverty line or speak a foreign language at home? (Enter your answer to one decimal place.) % (e) What percent of Americans live above the poverty line and only speak English at home? (Enter your answer to one decimal place.) events are

Answer 1

Living below the poverty line and speaking a foreign language at home are not disjoint. The Venn diagram shows the variables and their associated probabilities. The percentages of Americans who live below the poverty line and only speak English at home, who live below the poverty line or speak a foreign language at home, and who live above the poverty line and only speak English at home are 10.1%, 34.8%, and 89.9% respectively.

Step-by-step explanation:

(a) Living below the poverty line and speaking a foreign language at home are not disjoint. This means there are people who fall into both categories. In this case, the overlap between the two categories is 4.6%.

(b) Here is a Venn diagram summarizing the variables and their associated probabilities:

(c) To find the percent of Americans who live below the poverty line and only speak English at home, we need to subtract the percentage of Americans who speak a foreign language at home from the percentage who live below the poverty line: 14.7% - 4.6% = 10.1%.

(d) To find the percent of Americans who live below the poverty line or speak a foreign language at home, we need to add the percentages: 14.7% + 20.1% = 34.8%.

(e) To find the percent of Americans who live above the poverty line and only speak English at home, we subtract the percentage of Americans who live below the poverty line and only speak English at home from 100%: 100% - 10.1% = 89.9%.