Question
list 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. on 2 Does the procedure represent a binomial distribution? on 3 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 Gibson Harmon. in the United States
Feb 13,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The procedure does not represent a binomial distribution because the probability of success differs from trial to trial.
Solution
To determine whether the YSORT method of sex selection results in a binomial distribution, we need to evaluate the criteria for a binomial distribution:
1. **Fixed number of trials (n)**: The procedure involves 90 couples giving birth to 90 babies, which is a fixed number of trials.
2. **Two possible outcomes**: Each trial (birth) can result in either a boy (success) or a girl (failure). This satisfies the requirement of having two possible outcomes.
3. **Constant probability of success (p)**: The probability of having a boy (success) should remain constant for each trial. If the YSORT method is effective, we can assume that the probability of success is the same for each birth.
4. **Independent trials**: The outcome of one trial (the sex of one baby) should not affect the outcome of another trial.
Now, let's analyze the options provided:
A. **No, because there are more than two categories for each trial.**
- This is incorrect because there are only two categories (boy or girl).
B. **No, because the probability of success differs from trial to trial.**
- This could be true if the YSORT method does not guarantee a constant probability of having a boy for each birth. If the method is effective, we would expect a constant probability.
C. **Yes, because the procedure satisfies all the criteria for a binomial distribution.**
- This could be true if the probability of success is constant and trials are independent.
D. **No, because the trials of the procedure are not independent.**
- This could be true if the outcome of one birth affects the outcome of another, but typically, the sex of one baby does not influence the sex of another.
Based on the analysis, the most likely answer is:
**B. No, because the probability of success differs from trial to trial.**
This is because if the YSORT method does not ensure a constant probability of having a boy for each birth, it would not satisfy the criteria for a binomial distribution.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
The YSORT method introduces a scenario that can potentially violate the requirements for a binomial distribution. Specifically, the probability of having a boy or a girl may not remain constant across each birth if the method's effectiveness is not uniform or if external factors influence the sex ratio. In a binomial distribution, we need fixed trials, two outcomes (success or failure), constant probabilities, and independence of trials. Since the success of the YSORT method may vary among different couples, this affects the consistency in probabilities, leading to option B as the correct choice.
