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 200 couples use the ysort method and give birth to 200 babies, the sex of the babies is recorded. does the procedure represent a binomial distribution? o a. no, because the probability of success differs from trial to trial. o b. no, because there are more than two categories for each trial. o c. yes, because the procedure satisfies all the criteria for a binomial distribution. o d. no, because the trials of the procedure are not independent.

Explanation:

Step1: Check binomial distribution criteria

A binomial distribution has the following criteria:

• Fixed number of trials ($n = 200$ in this case).
• Each trial has two possible outcomes (boy - success or girl - failure).
• The probability of success ($p$, probability of a boy) is the same for each trial.
• Trials are independent (the sex of one baby does not affect the sex of another).

Step2: Analyze each option

• Option A: The probability of success (a boy) is the same for each trial (assuming the YSORT method's probability remains constant for each couple's attempt), so this option is incorrect.
• Option B: There are only two outcomes (boy or girl) for each trial (baby), so this option is incorrect.
• Option C: The procedure satisfies all binomial distribution criteria (fixed $n = 200$, two outcomes per trial, constant probability, independent trials).
• Option D: The trials (each couple having a baby) are independent (the result of one couple's baby's sex does not affect another's), so this option is incorrect.

Answer:

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