Question

determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). if the procedure is not binomial, identify at least one requirement that is not satisfied. the ysort method of sex - selection, developed by the genetics & ivf institute, was designed to increase the likelihood that a baby will be a boy. when 100 couples use the ysort method and give birth to 100 babies, the sex of the babies is recorded. does the procedure represent a binomial distribution? a. no, because there are more than two categories for each trial. b. no, because the probability of success differs from trial to trial. c. no, because the trials of the procedure are not independent. d. yes, because the procedure satisfies all the criteria for a binomial distribution.

Explanation:

Step1: Recall binomial distribution criteria

A binomial distribution has a fixed number of independent trials, two possible outcomes per trial, and a constant probability of success for each trial.

Step2: Analyze the given scenario

Here, there are $n = 100$ couples (fixed - number of trials). Each trial (birth of a baby) has two outcomes (boy or girl). The YSORT method is designed to change the probability of having a boy, but for each individual trial, the probability of having a boy is assumed to be constant across all 100 trials, and the birth of one baby is independent of the birth of another baby.

Answer:

D. Yes, because the procedure satisfies all the criteria for a binomial distribution