Sampling Distributions

Question

A student running for a position in student government believes that 55% of the student body will vote for her. However, she is worried about low voter turnout. n = 200. Complete parts a through d below.

I got parts a and b which is finding the mean and standard deviation, but cannot seem to find c and d. Please show how you got it!

c. How likely is it that she will not get the majority of the vote, that is, a sample proportion of 50% or lower from the 100 votes cast?

d. If instead n = 600 students show up for voting, how likely is it then that she will not win majority?

Answer 1

here n is large enough to consider that the distribution is normal. so assuming n = 200 and 55% in favor makes the mean µ = 200 (.55) = 110 and the standard deviation σ = √(200(.55)(.45)) using these mean and standard deviation for part c

P( x < 100)

and for part d : (μ = 330)

P(x < 300 )