Question

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.
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?

Answer 1

Answer:

b. 10.4

c.  26.9

Step-by-step explanation:

Let the universal set U = 100% which is the total no of people in the American community

Let A = 14.6% which is the total no of people living below poverty line

Let B = 20.7% which is the total no of people speaking foreign Language

C = 4.2% no of people who both speak foreign language and live below poverty line

X = no of people who neither live below poverty line nor speak foreign language

P (A) = 14.6%

P (B) = 20.7%

P (C) = P (A ∩ B) = 4.2%

P (A – C) = P (A ∩ U) = 14.6 – 4.2 = 10.4%

P (B – C) = P (B ∩ U) = 20.7 – 4.2 = 16.5%

P (X) = P (A ᴜ B) c =100 – (10.4 + 4.2 + 16.5) = 68.9%

a. The venn diagram is as shown above

b. Percent of Americans who live below poverty line and Speak English at home(minus foreign lang speakers living below poverty line) that is A only

= A – C

= 14.6 – 4.2

= 10.4%

c. Percentage of Americans Living below poverty line or Speaking foreign language

= A only + B only

A only = A – C ( People living below poverty line only)

= 14.6 -4.2

= 10.4%

B only = B – C ( people speaking foreign languages only)

= 20.7 – 4.2

= 16.5%

Hence

A only + B only = 10.4 + 16.5 = 26.9%

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