Suppose 58% of the registered voters in a country are Republican. If a sample of 536 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by greater than 5%

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13-07-2022
Mathematics

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Suppose 58% of the registered voters in a country are Republican. If a sample of 536 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by greater than 5%

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aroranishant799 aroranishant799 · Answer 1 · 2022-07-16T07:38:13+02:00

The probability that the sample proportion of Republicans will differ from the population proportion by greater than 5% is 100%

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

It is given that 58% of voters are Republican. The sample is 536 voters.

0.58×536 = 310.88 can be rounded off to 311.

536 - 311 = 225 are not republicans

311-225 = 86 is the difference

[tex]\frac{86}{536}[/tex]×100 = 16.044%

Hence, the probability is 100%.

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