Suppose 45% of voters favor candidate A.We can be 67% sure that out of 200 randomly selected voters, at least how many will favor candidate A?
A) 90
B) 87
C) 134
D) 93

Question

Quizplus · Accepted Answer

To determine the minimum number of voters who favor candidate A with 67% confidence, we can use the normal approximation to the binomial distribution.

First, we calculate the expected value of the number of voters who favor candidate A:

E(X) = np = 200 * 0.45 = 90

Next, we calculate the standard deviation of the number of voters who favor candidate A:

SD(X) = sqrt(np(1-p)) = sqrt(200 * 0.45 * 0.55) ≈ 7.13

Using the normal approximation, we can now find the number of voters who favor candidate A with at least 67% confidence by finding the z-score that corresponds to a cumulative probability of 0.67 in the standard normal distribution.

z = invNorm(0.67) ≈ 0.44

Now we can use this z-score to calculate the minimum number of voters who favor candidate A:

X = E(X) + z * SD(X) = 90 + 0.44 * 7.13 ≈ 87

Therefore, we can be 67% sure that out of 200 randomly selected voters, at least 87 will favor candidate A.

Suppose 45% of Voters Favor Candidate A