Pregunta
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
recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of
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
Responder
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:
- Fixed Number of Trials (
): There are a set number of trials. - Two Possible Outcomes: Each trial results in either a “success” or a “failure.”
- Constant Probability (
): The probability of success remains the same for each trial. - Independence: The outcomes of the trials are independent of each other.
Application to the Given Scenario
-
Fixed Number of Trials (
): - The hospital is caring for 5 babies.
- Therefore,
.
-
Two Possible Outcomes:
- Success: A baby recovers fully.
- Failure: A baby does not recover fully.
-
Constant Probability (
): - The probability of a baby recovering fully is 80%, so
. - Consequently, the probability of not recovering is
.
- The probability of a baby recovering fully is 80%, so
-
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.
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
Como
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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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