Statistics Help Requested (Discrete Distributions)

In summary, the problem involves an airline overbooking a flight with 100 tickets sold for 95 seats. The probability of an individual not showing up is 0.05, and the question is to find the probability of accommodating all passengers who show up. The equations used are Binomial and Poisson. The attempt at a solution involves finding the sum of probabilities for 4, 3, 2, 1, and 0 passengers not showing up.
  • #1
nichojo
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Homework Statement



The problem:

An airline always overbooks, if possible. A particular plane has 95 seats on a flight and the airline sells 100 tickets.

If the probability of an individual not showing is 0.05, assuming independence, what is the probability that the airline can accommodate all the passengers who show up?

Homework Equations



Binomial and Poisson

The Attempt at a Solution



I tried taking the sum from 1 to 95 (X<=95) with a choose of (100, x) * (.95)^x * (.05)^(100-x)

with no luck. I've also tried numerous other sequences, but I feel I'm stuck.

Thanks in advance.
 
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  • #2
What is the probability that 4 don't show up? 3? 2? 1? 0? Add them up.
 

What is a discrete distribution?

A discrete distribution is a statistical distribution that represents the probability of occurrence of discrete outcomes, such as the number of heads in multiple coin tosses or the number of children in a family. It is characterized by finite or countably infinite possible values and can be graphically represented by a histogram or bar chart.

What are some common discrete distributions?

Some common discrete distributions include the binomial distribution, Poisson distribution, and geometric distribution. The binomial distribution is used to model the number of successes in a fixed number of independent trials. The Poisson distribution is used to model the number of times an event occurs in a fixed interval of time or space. The geometric distribution is used to model the number of trials needed to achieve the first success in a sequence of independent trials.

How is a discrete distribution different from a continuous distribution?

A discrete distribution represents outcomes that can only take on certain values, whereas a continuous distribution represents outcomes that can take on any value within a given range. This means that a continuous distribution has an infinite number of possible values, while a discrete distribution has a finite or countably infinite number of possible values.

What is the importance of understanding discrete distributions?

Understanding discrete distributions is important in many fields, including statistics, economics, and engineering. It allows researchers to make predictions about the likelihood of certain outcomes and to make informed decisions based on these predictions. Discrete distributions also provide a way to analyze and interpret data, which is crucial in making evidence-based decisions.

How can I use statistics to analyze a discrete distribution?

To analyze a discrete distribution, you can use various statistical methods, such as calculating measures of central tendency (e.g. mean, median, mode) and measures of variability (e.g. range, standard deviation). You can also create visual representations of the distribution, such as histograms or bar charts, to better understand the data. Additionally, you can use statistical software or calculators to perform more advanced analyses, such as hypothesis testing and confidence interval estimation.

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