Question content area top
Part 1
A student running for a position in student government believes that
5353%
of the student body will vote for her. However, she is worried about low voter turnout. Complete parts a through d below.Question content area bottom
Part 1
a. Assuming she truly has
5353%
support in the entire student body, find the mean and standard deviation of the sampling distribution for the proportion of votes she will receive if only
nequals=200200
students show up for voting.
meanequals=. 53.53,
standard
deviationequals=. 035.035
(Round to three decimal places as needed.)
Part 2
b. Is it reasonable to assume a normal shape for this sampling distribution? Explain.
Since there are
106106
expected votes for the student and
9494
expected votes not for the student, it
is
reasonable to assume a normal shape.
(Type integers or decimals. Do not round.)
Part 3
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
200200
votes cast?
The probability is
0.19570.1957.
(Round to four decimal places as needed.)
Part 4
d. If instead
nequals=10001000
students show up for voting, how likely is it then that she will not win the majority?
The probability is
0.02870.0287.