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
Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, is designed to increase the likelihood that a baby will be a boy. When 291 couples use the YSORT method and give birth to 291 babies, the genders of the babies are recorded.
To be a binomial probability distribution, a procedure must satisfy the preceding four requirements:
1. The procedure has a fixed number of trials. Here, 291 couples use the YSORT method of gender selection.
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, gender of the children (outcomes) can be classified into two categories, male and female.
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.