A political pollster is conducting an analysis of sample results in order to mak
ID: 3359851 • 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 54% of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 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%?
(ANSWERED ALREADY) The probability is .2177 that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%. (Round to four decimal places as needed.)
b. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 59%?
The probability is _______ that a candidate will be forecast as the winner when the population percentage of her vote is 59%. (Round to four decimal places as needed.)
Explanation / Answer
b)here p=0.59 and n=100
std error =(p(1-p)/n)1/2 =0.0492
therefore probability that a candidate will be forecast as the winner when the population percentage of her vote is 59% =P(X>0.54)=1-P(X<0.54)=1-P(Z<(0.54-0.59)/0.0492)=1-P(Z<-1.0166)=1-0.1547 =0.8453
The probability is 0.8453 that a candidate will be forecast as the winner when the population percentage of her vote is 59%