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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 90 couples use the YSORT method and give birth to 90 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. Yes, because the procedure satisfies all the criteria for a binomial distribution. D. No, because the trials of the procedure are not independent.

Ask by Adkins Welch. in the United States
Feb 13,2025

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Answer

The procedure represents a binomial distribution because it meets all the criteria: two possible outcomes, constant probability of success, and independent trials.

Solution

To determine whether the YSORT method of sex selection represents a binomial distribution, we need to check if it satisfies the criteria for a binomial distribution. A binomial distribution is characterized by the following criteria: 1. Each trial must have only two possible outcomes (success or failure). 2. The probability of success must be the same for each trial. 3. The trials must be independent of each other. Let's analyze the given procedure: 1. Each trial (giving birth to a baby) has only two possible outcomes: boy or girl. 2. The probability of success (having a boy) is the same for each trial, as the YSORT method is designed to increase the likelihood of having a boy. 3. The trials (giving birth to 90 babies) are independent of each other. Based on the analysis, the YSORT method of sex selection satisfies all the criteria for a binomial distribution. Therefore, the procedure represents a binomial distribution. The correct answer is: C. Yes, because the procedure satisfies all the criteria for a binomial distribution.

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B. No, because the probability of success differs from trial to trial. In a binomial distribution, the probability of each outcome (in this case, having a boy) must remain constant across trials. If the YSORT method influences the likelihood of the baby's sex differently for each couple, then we can't treat this scenario as a binomial distribution, leading to varying probabilities across the 90 births. Additionally, to have a true binomial distribution, each trial must be independent of the others. If the YSORT method causes some dependency among the outcomes, that would violate the independence requirement, making it inappropriate for applying binomial theory here.

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