Question

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?

Answer 1

@jim_thompson5910 ,

Answer 2

this is a binomial distribution problem

Answer 3

5.1%
10%
27%
15%

Answer 4

in this case, n = 10, p = 0.76 and k = 5

Answer 5

Do u have any idea of binomail probability distribution ?

Answer 6

so @jim_thompson5910 is 5% my answer?

Answer 7

P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)


P(X = 5) = (10 C 5)*(0.76)^(5)*(1-0.76)^(10-5)


P(X = 5) = (10 C 5)*(0.76)^(5)*(0.24)^(10-5)


P(X = 5) = (252)*(0.76)^(5)*(0.24)^5


P(X = 5) = (252)*(0.253553)*(0.000796)


P(X = 5) = 0.050877


So it's closest to 5.1% after rounding

Answer 8

Thank you @jim_thompson5910