Question

n a certain congressional district, it is known that 60% of the registered voters classify themselves as conservatives. If ten registered voters are selected at random from this district, what is the probability that four of them will be conservatives

Answer 1

Explanation:

Let x be a random variable representing the number of registered voters in the congressional district. This is a binomial distribution since the outcomes are two ways. It is either a randomly selected registered voter is a conservative or not. The success would be that a randomly selected voter is a conservative. The probability of success, p = 60/100 = 0.6

The probability of failure, q would be 1 - p = 1 - 0.6 = 0.4

Given n = 10, we want to determine P(x = 4)

From the binomial distribution calculator,

P(x = 4) = 0.11