Question

suppose that 9 people, chosen at random, are asked if they favour a certain proposal. find the probability that majority of the persons polled will favour proposal, given that 45 percent of the population favour the proposal

Answer 1

Given: n = 9

P=0.45

Since the experiment consists of n identical trials. Each trial results in one of the two outcomes, called success and failure. The probability of success, denoted p, remains the same from trial to trial, we use binomial distribution here.

To find :The probability that majority of the persons polled will favour proposal. Persons polled will favor proposal in majority when x$\geq$ 5

that is P(X$\geq$5)

solution:

P(x$\geq$ 5)= 1- P(X<5)

= 1- P(X $\leq$ 4)

= 1- 0.6214

=0.3786

Answer: the probability that majority of the persons polled will favour proposal, given that 45 percent of the population favour the proposal is 0.3786.