Question

assume that the number of votes for a school board candidate follows a binomial distribution with pi=0.55. write out the notation, but do not bother solving, for the probability that the candidate wins the election that has 99 votes casted. also, comment on if the probability this candidate wins the election will either go up, down, or stay the same if pi still equals 0.55, but the sample size significantly increases

Answer 1

n, be the number of students in the school

probability, p = 0.55

Candidate win if he gets 99 votes

Probability of getting 99 votes = nC99*p^99*(1-p)^(n-99) , where nCk is n combination

if sample size increases the probability of winning of candidate will increase, since the number of votes required to win the election is 99 and the probability is also the same as 0.55, but the n increases and the value nCk increases