Answer:
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
