A political pollster is conducting an analysis of sample results in order to mak

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%

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