Question

17. Ease of Voting Twenty-seven percent of likely U.S. voters think that it is too easy to vote in the United States. You randomly select 12 likely U.S voters. Find the probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is (a) exactly three, (b) at least four, and (c) less than eight. (Source: Rasmussen Reports)

Answer 1

X ~ Binomial ( n , p)

Where n = 12, p = 0.27

Binomial probability distribution is

P(X) = ⁿC_x p^x (1-p)^n-x

a)

P(X = 3) = ¹²C₃ 0.27³ 0.73⁹

= 0.2547

b)

P( X >= 4) = 1 - P( X <= 3)

= 1 - [ P( x = 0) + P( X = 1) + P( X = 2) + P( X = 3) ]

= 1 - 0.7096

= 0.2904

c)

P( X < 8) = 1 - p( X >= 8)

= 1 - [ P( X = 8) + P( X = 9) + P( X = 10) + P( X = 11) + P( X = 12) ]

= 1 - 0.0016

= 0.9984