Question

32?% of a certain? country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is? (a) exactly? three, (b) at least? four, (c) less than eight.

Answer 1

This is a binomial distribution with p = 0.32 and n = 12

Let X = the number of voters who think that it's too easy to vote

a) P(X = 3) = = 0.224

b) P(X atleast 4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)] = 1 - [ ]

= 1 - [ 0.00977 + 0.0552 + 0.143 + 0.224 ] = 0.56803

c) P(X < 8) = P(X=0) + P(X=1) .... + P(X=7)

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

= 1 - [ ]

= 1 - [ 0.0116 + 0.00243 + 0.000343 + 0.000029 + 0.00000115 ]

= 1 - 0.0144 = 0.9856

Cheers!

Upvote if this was helpful.