A poll shows that 76% of voters favor an initiative. If 7 voters are selected at random, what is the
probability that exactly 4 of them will vote in favor? (1 point)
About 35%
About 16.1%
About 3.87%
About 76%
About 16.1%
To calculate this probability, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * q^(n-k), where
n = 7 (total number of voters selected)
k = 4 (number of voters in favor)
p = 0.76 (probability of a voter favoring the initiative)
q = 1 - p = 0.24 (probability of a voter not favoring the initiative)
Plugging in the values, we get:
P(X = 4) = (7 choose 4) * (0.76)^4 * (0.24)^(7-4)
P(X = 4) = 35 * 0.276675584 * 0.13824
P(X = 4) ≈ 0.161
So, the probability that exactly 4 of the 7 selected voters will vote in favor is about 16.1%.