In a certain congressional district, it is known that 20% of the registered voters classify themselves as conservatives. If ten registered voters are selected at random from this district, what is the probability that six of them will be conservatives

Step-by-step explanation:

We would assume that a randomly selected registered voter, x is classified as a conservative or not. It means that there are only 2 possible outcomes. Thus, it is a binomial probability distribution and the probability of success, p is that a randomly selected voter is classified as a conservative. Therefore,

p = 20% = 20/100 = 0.2

Number of trials, n = 10

Number of success, x = 6

The probability that six out of 10 would be conservatives is expressed as

P(x = 6)

Using the binomial probability calculator,

P(x = 6) = 0.0056