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 50 couples use the ysort method and give birth to 50 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:

1. Recall the criteria for a binomial distribution: fixed number of trials ($n = 50$ couples having babies), two - possible outcomes (baby is a boy or a girl), independent trials (the sex determination of one baby does not affect the sex determination of another baby), and constant probability of success (the probability of having a boy using the YSORT method is assumed to be constant for each couple).
2. Analyze each option:

• Option A: There are only two categories (boy or girl) for each trial, so this is incorrect.
• Option B: The YSORT method is intended to give a certain probability of having a boy, and this probability is assumed to be the same for each couple (trial), so this is incorrect.
• Option C: The birth of one baby does not affect the birth of another baby, so the trials are independent, so this is incorrect.
• Option D: The procedure satisfies all the criteria for a binomial distribution: fixed number of trials ($n = 50$), two possible outcomes, independent trials, and constant probability of success.

Answer:

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