In a USA TODAY/Gallup Poll, respondents favored Barack Obama over Mitt Romney in terms of likeability, 61% to 32% (Los Angeles Times, July 28, 2012). a. What percentage of respondents favored neither Obama nor Romney in terms of likeability? Percentage of respondents b. For a given survey of 500, how many more respondents favored Obama than Romney? Number of respondents

a) percentage of respondents that favored neither Obama nor Romney in terms of likeability = 7%

b) For a given survey of 500, the number of respondents that favored Obama than Romney is 145.

Step-by-step explanation:

Given that none of those surveyed can favour the two candidates at the same time,

n (Universal set) = n (U) = 100%

n (Obama) = n (O) = 61%

n (Romney) = n (R) = 32%

n (That favour Obama and Romney) = n (O n R) = 0%

To calculate for the number that favour neither of the candidates

n (O' n R')

n (U) = n (O) + n (R) + n (O n R) + n (O' n R')

100 = 61 + 32 + 0 + n (O' n R')

n (O' n R') = 100 - 93 = 7%

b) For a given survey of 500, how many more respondents favored Obama than Romney?

Number of those surveyed that favour Obama = 61% of 500 = 305

Number of those surveyed that favour Romney = 32% of 500 = 160

Difference = 305 - 160 = 145