Pregunta
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About of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment. The random variable represents the number of babies that
recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of , , and , and list the possible values of the random variable
.
Is the experiment a binomial experiment?
Yes
No

Ask by Frazier Owen. in the United States
Jan 21,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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Yes, the experiment is a binomial experiment.
  • Success: A baby recovers fully.
  • Number of trials (n): 5
  • Probability of success §: 0.8
  • Probability of failure (q): 0.2
  • Possible values of : 0, 1, 2, 3, 4, 5

Solución

Yes, the experiment is a binomial experiment. Here’s the breakdown:

Criteria for a Binomial Experiment

A binomial experiment must satisfy the following conditions:
  1. Fixed Number of Trials ( ): There are a set number of trials.
  2. Two Possible Outcomes: Each trial results in either a “success” or a “failure.”
  3. Constant Probability ( ): The probability of success remains the same for each trial.
  4. Independence: The outcomes of the trials are independent of each other.

Application to the Given Scenario

  1. Fixed Number of Trials ( ):
    • The hospital is caring for 5 babies.
    • Therefore, .
  2. Two Possible Outcomes:
    • Success: A baby recovers fully.
    • Failure: A baby does not recover fully.
  3. Constant Probability ( ):
    • The probability of a baby recovering fully is 80%, so .
    • Consequently, the probability of not recovering is .
  4. Independence:
    • Assuming that the recovery of one baby does not influence the recovery of another, the trials are independent.

Summary of Binomial Parameters

  • Success Definition: A baby recovers fully.
  • Number of Trials ( ): 5
  • Probability of Success ( ): 0.8
  • Probability of Failure ( ): 0.2
  • Possible Values of the Random Variable ( ): This represents the number of babies (out of five) that recover fully.

Conclusion

All the criteria for a binomial experiment are met in this scenario. Therefore, it is indeed a binomial experiment.
Answer:
Yes, the experiment is a binomial experiment.
  • Success: A baby recovers fully.
  • Number of trials (n): 5
  • Probability of success §: 0.8
  • Probability of failure (q): 0.2
  • Possible values of : 0, 1, 2, 3, 4, 5

Respondido por UpStudy AI y revisado por un tutor profesional

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Extra Insights

Yes, this experiment is a binomial experiment! In a binomial experiment, we have fixed trials, two possible outcomes (success or failure), constant probability of success, and independent trials. Here, the success is defined as a baby recovering fully.
For this scenario, (the number of babies), (the probability of recovery), and (the probability of not recovering). The possible values of the random variable , which represents the number of babies that recover, can be or .

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