Among 15,378 Delta airline passengers randomly selected, 3 were bumped from a flight against there wishes (based on data from the us dept of transportation) find the probability that a random selected passenger is involuntarily bumped. Is such bumping unusual? Does such bumping pose a serious problem for Delta passengers in general? why or why not? what is the method used to obtain the probability?
3/15,378 = .0002
That should help you answer the questions.
To find the probability that a randomly selected passenger is involuntarily bumped, we need to divide the number of passengers who were involuntarily bumped by the total number of passengers:
Probability of being involuntarily bumped = Number of involuntarily bumped passengers / Total number of passengers
In this case, the number of passengers who were involuntarily bumped is 3, and the total number of passengers is 15,378. Therefore, the probability is:
Probability of being involuntarily bumped = 3 / 15,378
To determine if such bumping is unusual or poses a serious problem for Delta passengers in general, we need to compare the obtained probability with some benchmark or industry standards. Unfortunately, since no specific benchmark is provided in the question, we cannot make a definitive judgment on whether it is unusual or poses a serious problem. However, we can state that the probability is very low, indicating that the chances of being involuntarily bumped are slim.
The method used to obtain the probability is simply dividing the number of passengers who were involuntarily bumped by the total number of passengers. This formula is commonly used to determine probabilities in statistics.
To find the probability that a randomly selected passenger from the 15,378 Delta airline passengers is involuntarily bumped, we need to determine the ratio of bumped passengers to the total number of passengers selected.
Probability is defined as the number of favorable outcomes divided by the number of possible outcomes. In this case, the number of favorable outcomes is 3 (the number of passengers who were involuntarily bumped) and the number of possible outcomes is 15,378 (the total number of randomly selected passengers).
Therefore, the probability of a randomly selected passenger being involuntarily bumped is:
Probability = Number of favorable outcomes / Number of possible outcomes
= 3 / 15,378
≈ 0.000195
This means that the probability of a randomly selected passenger being involuntarily bumped is approximately 0.000195 or 0.0195%.
To determine if such bumping is unusual, we can compare the probability to a threshold or benchmark. However, what is considered unusual or normal depends on the context and industry standards. Generally, a probability of less than 5% is often considered to be an indication of an unusual event.
In this case, the probability of 0.0195% indicates that the likelihood of a randomly selected passenger being involuntarily bumped is extremely low. As such, we can conclude that such bumping is indeed unusual.
As for whether this poses a serious problem for Delta passengers in general, we need to consider the magnitude and impact of the bumping incidents relative to the total number of passengers. Since only 3 out of 15,378 passengers were involuntarily bumped, we can infer that the problem is not widespread or common for Delta passengers.
However, it is important to note that while the probability is low and the problem may not be significant for most passengers, the experience of being involuntarily bumped can still be disruptive and inconvenient for those individuals affected.
The method used to obtain the probability is based on the provided data and the concept of probability. By determining the ratio of favorable outcomes (3) to the total number of outcomes (15,378), we can calculate the probability of a randomly selected passenger being involuntarily bumped.