Question

A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important.

Which distribution should you use for this problem?
a) Normal distribution
b) Binomial distribution
c) Poisson distribution
d) Uniform distribution

Answer 1

The distribution that should be used for this problem is the binomial distribution.

Step-by-step explanation:

The random variable X represents the proportion of voters who believe the economy is the most important. The binomial distribution is suitable as the poll involved a fixed number of voters (1,200), and each voter had two possible outcomes – either considering the economy the most important or not. The sample size is reasonably large, meeting the conditions for the Central Limit Theorem, allowing us to approximate the binomial distribution with a normal distribution. This makes calculations more tractable. Therefore, the binomial distribution is an appropriate model for estimating the proportion of voters prioritizing the economy in the upcoming election.