Question

g Determine if the following probability experiments represents a binomial experiment. Explain your answer as to why or why not. a) A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security. b) A baseball player who reaches base safely 30% of the time is allowed to bat until he reaches base safely for the third time. The number of at-bats required is recorded.

Answer 1

a) It is a binomial experiment

b) It is not a binomial experiment, since we do not have a value of n.

Explanation:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

So:

a) A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should reform Social Security.

For each voter, there are only two outcomes. Either they believe the Congress should reform Social Security, or they do not believe.

There are 1200 voters, so
`n = 1200`.

Each voter has a probability of voting yes and a probability of voting no. So yes, it is a binomial experiment.

b) A baseball player who reaches base safely 30% of the time is allowed to bat until he reaches base safely for the third time. The number of at-bats required is recorded.

Here, there is no fixed number of at bats, so there is no value of n. So this is not a binomal experiment.