i wish i could say i knew somewhat of where to start for these problems but i dont. My teacher is not the best and the homeworks are always ridiculous, but im not here to whine, im here looking for some help, does anyone know what to do for any of these? Thanks alot for help
Intuitively, the expected number of votes for A is the total number of votes * probability of A winning each vote = n*p = 60000 * 0.5 = 30000
Using, more formal notation, the number of votes for A is a binomial variable. n = 60000 trials. p = 0.5 (per-vote probability of winning that vote). Expected value of such a variable is n*p = 30000.
Again, viewing the number of votes for A as a binomial variable with n = 60000 trials and p = 0.5, variance is n*p*(1-p). Standard deviation is square root of that variance.
You either need to use a look up table in a book or use a binomial distribution calculator of some kind. You can use the R command: pbinom(27000, 60000, 0.5) or something like http://stattrek.com/Tables/Binomial.aspx
The answer is a probability of 0 that candidate B would get less than 27000 votes out of 60000 total if each vote really did have a 50/50 chance of being for candidate B.
It is not consistent and is highly unlikely given the 50/50 assumption.
The probability that Z is greater than 2.05 is less than or equal to the probability that Z is greater or equal to 2.05. This should be fairly intuitive...
I didn't do problem 3 yet. Let me know if this is helpful thus far.