Identifying Binomial Distributions. In Exercises, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at hast one requirement that is not satisfied
Veggie Survey In an Idaho Potato Commission survey of 1000 adults, subjects are asked to select their favorite vegetables, and each response was recorded as “potatoes” or “other.”
To be a binomial probability distribution, a procedure must satisfy the preceding four requirements:
1. The procedure has a fixed number of trials. Here, 1000 subjects were asked to select their favorite vegetables.
2. The trials must be independent. Here, we assume that the population is very large and the sample size is less than 5% of the population. So, from the 5% Guideline for Cumbersome Calculations, if a sample size is no more than 5% of the size of the population, we can treat the selections as being independent.
3. Each trial must have all outcomes classified into two categories. Here, responses were recorded into two categories, potatoes and other.
4. The probability of success remains the same in all trials.
Since all four requirements are satisfied. So, this is a distribution that can be treated as binomial.