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2.8 Poverty and language. The American Community Survey is an ongoing survey that provides data every year to give communities the current information they need to plan investments and services. The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English (foreign language) at home, and 4.2% fall into both categories.59 (a) Are living below the poverty line and speaking a foreign language at home disjoint

a) Draw a Venn diagram summarizing the variables and their associated probabilities

b) What percent of Americans live below the poverty line and only speak English at home?

c) What percent of Americans live below the poverty line or speak a foreign language at home?

Respuesta :

Answer:

a) No, living below the poverty line and speaking a foreign language at home are not disjoint.

A) The Venn diagram is presented in the attached image to this solution

B) percent of Americans living below the poverty line and only speak English at home = 10.4%

C) The percent of Americans living below the poverty line or speak a foreign language at home = 31.1%

Step-by-step explanation:

Let the set of people living below the poverty line be represented by L

And the set of people speaking a foreign language at home be represented by S

P(L) = 14.6% = 0.146

P(S) = 20.7% = 0.207

P(L n S) = 4.2% = 0.042

The set of complements, that is, set of people not living below the poverty line is L'. P(L') = 100 - 14.6 = 85.4% = 0.854

And the set of people that speak English at home is S'. P(S') = 100 - 20.7 = 79.3% = 0.793

a) No, living below the poverty line and speaking a foreign language at home are not disjoint.

This is because the living below the poverty line and speaking a foreign language are events that have elements in common, that is, one variable falls in the other one. they are not disjoint events.

A) The Venn diagram is presented in the attached image to this solution

B) The percent of Americans living below the poverty line and only speak English at home = P(L n S') = P(L) - P(L n S) = 0.146 - 0.042 = 0.104 = 10.4%

C) percent of Americans living below the poverty line or speak a foreign language at home P(L u S) = P(L n S') + P(L' n S) + P(L n S)

P(L n S') = P(L) - P(L n S) = 0.104

P(L' n S) = P(S) - P(L n S) = 0.207 - 0.042 = 0.165

P(L n S) = 0.104

P(L u S) = P(L n S') + P(L' n S) + P(L n S) = 0.104 + 0.165 + 0.042 = 0.311 = 31.1%

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