27.4%
To calculate this probability, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n = number of trials (10 voters selected), k = number of successful outcomes (5 voters in favor), p = probability of success on any given trial (76% or 0.76).
Plugging in these values:
P(X = 5) = (10 choose 5) * 0.76^5 * (1-0.76)^(10-5)
P(X = 5) = (252) * 0.76^5 * 0.24^5
P(X = 5) = 252 * 0.00780608 * 0.000796262
P(X = 5) ≈ 0.015674
Convert this to a percentage by multiplying by 100:
0.015674 * 100 ≈ 1.5674%
So the probability that exactly five out of ten voters will vote in favor of the initiative is approximately 1.57%, closest to 5.1%.
A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative?(1 point)
10%
15%
27.4%
5.1%
1 answer