Question A recent poxll found that 45% of eligible voters are planning to vote in favor of a new by-law. Suppose you randomly survey six voters. What is the probability that at least three of the voters plan to vote in favor of the new by-law? (1 point) Responses 13.2% 13.2% 25.5% 25.5% 30.3% 30.3% 55.8%
The probability of a voter planning to vote in favor of the new by-law is 0.45.
The probability of at least 3 out of 6 voters voting in favor can be calculated using the binomial probability formula:
P(X >= 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)
P(X = 0) = (6 choose 0) * (0.45)^0 * (0.55)^6 = 0.0083
P(X = 1) = (6 choose 1) * (0.45)^1 * (0.55)^5 = 0.0558
P(X = 2) = (6 choose 2) * (0.45)^2 * (0.55)^4 = 0.1783
P(X >= 3) = 1 - 0.0083 - 0.0558 - 0.1783
P(X >= 3) = 1 - 0.2424
P(X >= 3) = 0.7576
Therefore, the probability that at least three of the voters plan to vote in favor of the new by-law is 75.76%, which is closest to 75.8%.