Identifying Binomial Distributions. In Exercises 5–12, 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 least one requirement that is not satisfied.

Clinical Trial of YSORT The YSORT method of gender selection, developed by the Genetics & IVF Institute, was 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.

Out of 291 couples who used the YSORT method to give birth to 291 babies, the genders of the 291 babies are recorded.

The following assumptions of the binomial distribution should be satisfied:

• The procedure should have a finite number of trials.
• Independent trials
• Each trial should have outcomes that are of exactly two kinds: success and failure.
• The likelihood of success (denoted as p) remainsthe same for all the trials.

The number of trials is fixed and holds a value equal to 291.

All trials are independent as 291 different couples are used to produce 291 babies.

It can be seen that the trial involves recording the gender of the baby. Moreover, the gender of a baby has exactly two possible outcomes.

Since all the 291 couples have used the same YSORT method, the probability of success (boy) will remain the same for all trials.

Since the procedure follows all the above assumptions,the given situation can be modeled using the binomial distribution.