In a past election, the voter turnout was 68%. In a survey, 1000 sub ects were a

ID: 2948334 • Letter: I

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In a past election, the voter turnout was 68%. In a survey, 1000 sub ects were asked if th y voted in the election a Find the mean and st dad de at n fy the numbers of voters in groups of 1000. b. In the survey of 1000 people, 717 said that they voted in the election, Is this result consistent with the turnout, or is this result unlikely to occur with a turnout of 68%? why or why not? c Based on these results, does it appear that accurate voting results can be obtained by asing w ters how they acted? a. ? (Round to one decimal place as needed.) (Round to one decimal place as needed.) b. Is the result of 717 voting in the election usual or unusual? O A. This result is unusual because 717 is below the minimum usual value. O B. This result is usual because 717 is within the range of usual values ° C. This result is unusual because 717 is within the range of usual values. O D. This result is unusual because 717 is greater than the maximum usual value. e. Does it appear that accurate voting results can be obtained by asking voters how they acted? O B. No, because it appears that oubetantilly fewer people say that they voted than the proportion of people who actuaily did vote. actualy did vote A. Yes, because the results indicate that 68% rs a possible turnout. C. No, because it appears that substantially more people say that they voted than the proportion of people whe sibili unting

Explanation / Answer

Let X denote the number of voters in group of 1000.

Here, X follows normal approximation to the binomial distribution where n = 1000 and the voter turnout,p = 0.68

Thus, q = 1 - p = 0.32

(a) Mean, u = np = 1000*0.68 = 680

Variance= npq = 1000*0.68*0.32 = 217.6

Thus, standard deviation,s = ?217.6 = 14.75

(b) The range of usual values is { u - 2s, u + 2s } = { 650.5, 689.5}

Thus, the result is unusual because 717 is greater than the maximum usual value.( option D)

(c) No, the accurate voting results can not be obtained because it appears that substantially more people say that they voted than the proportion of people who actually did vote as the resulting number of 717 is unusual.

(option C)

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In a past election, the voter turnout was 68%. In a survey, 1000 sub ects were a

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