# Perception and Reality In a presidential election, 611 randomly selected voters were surveyed, and 308 of them said that they voted for the winning candidate (based on data from ICR Survey Research Group). The actual percentage of votes for the winning candidate was 43%. Assume that 43% of voters actually did vote for the winning candidate, and assume that 611 voters are randomly selected.a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the 308 voters who said that they voted for the winner significantly high?b. Find the probability of exactly 308 voters who actually voted for the winner.c. Find the probability of 308 or more voters who actually voted for the winner.d. Which probability is relevant for determining whether the value of 308 voters is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 308 voters who said that they voted for the winner significantly high?e. What is an important observation about the survey results?

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Perception and Reality In a presidential election, 611 randomly selected voters were surveyed, and 308 of them said that they voted for the winning candidate (based on data from ICR Survey Research Group). The actual percentage of votes for the winning candidate was 43%. Assume that 43% of voters actually did vote for the winning candidate, and assume that 611 voters are randomly selected.

a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the 308 voters who said that they voted for the winner significantly high?

b. Find the probability of exactly 308 voters who actually voted for the winner.

c. Find the probability of 308 or more voters who actually voted for the winner.

d. Which probability is relevant for determining whether the value of 308 voters is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 308 voters who said that they voted for the winner significantly high?

e. What is an important observation about the survey results?

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Step 1

a)

Define the random variable x as the number of votes for the winning candidate. Here, the number of voters selected at random (n) is 611 and every voter is independent of the other. Also, there are two possible outcomes (voted for the winning candidate and did not vote for the winning candidate) and the probability of voters who actually voted for the winning candidate (p) is 0.43. Thus, x follows the binomial distribution.

Step 2

Mean of Binomial distribution:

The formula is,

Step 3

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