A political pollster is conducting an analysis of sample results in order to mak
ID: 3203326 • Letter: A
Question
A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of 400 voters. Complete parts (a) through (c) below.
a.
What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%
b.
What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 56%
c.
What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 49%
a.
What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%
b.
What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 56%
c.
What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 49%
Explanation / Answer
a)n=400 sample size
mean=np = 400*.501 =200.4
sd=sqrt[np(1-p)]=sqrt[400(0.501)(0.499)]=9.99998
Assume normal distribution
z=(55-50.1)/9.99998= 0.49
p(x >= 55)= p(z > 0.49) =1-.70884= 0.29116
b) n=400 sample size
mean=np = 400*.56 =224
sd=sqrt[np(1-p)]=sqrt[400(0.56)(0.44)]=9.9277
Assume normal distribution
z=(55-56)/9.9277= -0.10072
p(x >= 55)= p(z > -0.1)= 1-0.55962=0.44038
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