Question 6 In an election, 53% of voters are expected to vote for candidate A. C
ID: 3057364 • Letter: Q
Question
Question 6
In an election, 53% of voters are expected to vote for candidate A. Consider a sample of 75 of those voters and answer the below questions.
Question 6 options:
A. _____
What is the standard deviation of the proportion of voters voting for candidate A from the sample?
B. _____
Consider the proportion of voters voting for candidate A from the sample of n=75 voters. What is the probability that the proportion is GREATER than 0.60?
C. _____
Consider the proportion of voters voting for candidate A from the sample of n=75 voters. What is the probability that the proportion is GREATER than 0.53?
D. _____
What is the mean of the distribution of the proportion of voters voting for candidate A from the sample?
Note: Below choices may NOT all be used as matches.
0.456
0.281
0.0576
0.11
0.50
0.530
No answer is correct.
A. _____
What is the standard deviation of the proportion of voters voting for candidate A from the sample?
B. _____
Consider the proportion of voters voting for candidate A from the sample of n=75 voters. What is the probability that the proportion is GREATER than 0.60?
C. _____
Consider the proportion of voters voting for candidate A from the sample of n=75 voters. What is the probability that the proportion is GREATER than 0.53?
D. _____
What is the mean of the distribution of the proportion of voters voting for candidate A from the sample?
1.Note: Below choices may NOT all be used as matches.
2.0.456
3.0.281
4.0.0576
5.0.11
6.0.50
7.0.530
8.No answer is correct.
Explanation / Answer
Given n = 75 and p = 0.53
Using Binomial distribution
A) SD = sqrt(npq) = sqrt(75*0.53*0.47) = 4.3223
B) P(P > 0.60) = P(Z > (0.60 - 0.53)/4.3223)) = P(Z > 0.016195) = 0.49354
C) Consider the proportion of voters voting for candidate A from the sample of n=75 voters. What is the probability that the proportion is GREATER than 0.53?
P(P > 0.53) = P(Z > (0.53 - 0.53)/4.3223)) = P(Z > 0) = 0.50
D) mean = np = 75*0.53 = 39.75
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