7.a.

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.

7.b.

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.

7.c

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.

7.d

It is not consistent and is highly unlikely given the 50/50 assumption.

4.

<=

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.