A poll is given, showing 40% are in favor of a new building project. If 5 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

the probability that exactly 4 of them favor the new building project is 0.0768

Step-by-step explanation:

We would assume a binomial distribution for the number of people that are in favor of a new building project. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 5

x = r = 4

Therefore,

P(x = 4) = 5C4 × 0.4^4 × 0.6^(5 - 4)

P(x = 4) = 5 × 0.0256 × 0.6

P(x = 4) = 0.0768

c - they will have the same distribution

step-by-step explanation:

this is the only one that could make sense. : )