In the upcoming governor's election, the most recent poll based on 900 respondents predicts that the incumbent will be reelected with 55% of the votes. for the sake of argument, assume that 51% of the actual voters in the state support the incumbent governor (p = 0.51). calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor.

Solution: We are given:

We have to find

Now we have to find the z score corresponding to

Using the standard normal table, we have:

Therefore, the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor is 0.0082

0.0081

Explanation:

Let p be the population proportion of voters in the state support the incumbent governor .

According to the given information , we have

Population proportion :

Sample size (Number of respondents): n= 900

Sample proportion of voters in the state support the incumbent governor :

Further  Explanation:

Formula to find z-score (for proportion) :  

[Rounded to the nearest two decimal places]

To find the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor , we find the p-value below :

[Rounded to the nearest 4 decimal places.]

Therefore , the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor = 0.0081

Refer the given attachment for further understanding.

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Keywords :

sample proportion , z-value , z-table , Normal curve.