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

Criteria for a Binomial Experiment

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

• 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