# Binomial Distribution Question

In summary, the question asks for an equation to estimate the probability of a patient remaining in fibrillation after N attempts, assuming that the probability of defibrillation on one attempt is independent of other attempts. The binomial distribution is used to model this equation, with the probability of remaining in fibrillation being 0.37 after one attempt and decreasing with each subsequent attempt. To estimate the probability of defibrillation, the equation p+q=1 is used.

## Homework Statement

The question provides a table and asks:

Number of Attempts Fraction persisting in fibrillation
0 1.00
1 0.37
2 0.15
3 0.07
4 0.02

"Assume that the probability p of defibrillation on one attempt is independent of other attempts. Obtain an equation for the probability that the patient remains in fibrillation after N attempts. Compare it to the data and estimate p."

## Homework Equations

Binomial Distribution

## The Attempt at a Solution

I used the binomial distribution for my equation to estimate the probability that the patient remains in fibrillation. I'm not concerned about the "number of successes" in each attempt, so I believe this problem is similar to asking a coin toss question. For example, the probability that a coin will return heads after 1 attempt is 0.50. After 2 attempts, 0.5*0.5, etc.

Likewise, there are two possibilities: fibrillation and defibrillation. Instead of the coin example, the probability that the patient remains in fibrillation is 0.37. After two attempts, 0.37*0.37. After 3 attempts, 0.37*0.37*0.37, etc. It models the data rather well.

So then to estimate "p", the probability of defibrillation in each, p+q = 1 ---> p= 1-q

Does this sound reasonable?

Obtain an equation for the probability that the patient remains in fibrillation after N attempts. Compare it to the data and estimate p."

## The Attempt at a Solution

I used the binomial distribution for my equation to estimate the probability that the patient remains in fibrillation. I'm not concerned about the "number of successes" in each attempt, so I believe this problem is similar to asking a coin toss question. For example, the probability that a coin will return heads after 1 attempt is 0.50. After 2 attempts, 0.5*0.5, etc.

Likewise, there are two possibilities: fibrillation and defibrillation. Instead of the coin example, the probability that the patient remains in fibrillation is 0.37. After two attempts, 0.37*0.37. After 3 attempts, 0.37*0.37*0.37, etc. It models the data rather well.

So then to estimate "p", the probability of defibrillation in each, p+q = 1 ---> p= 1-q

Does this sound reasonable?
The question asks for an equation. What is your equation for the probability that the patient remains in fibrillation after N attempts.

AM

## 1. What is a binomial distribution?

A binomial distribution is a probability distribution that describes the number of successes in a sequence of independent experiments or trials, where each trial can have only two possible outcomes (success or failure) and the probability of success remains constant throughout all trials.

## 2. How is a binomial distribution different from a normal distribution?

A normal distribution is a probability distribution that describes continuous data, while a binomial distribution is used for discrete data. Additionally, in a normal distribution, the mean, median, and mode are all equal, while in a binomial distribution, the mean and median may not be equal.

## 3. What are the main characteristics of a binomial distribution?

The main characteristics of a binomial distribution are the number of trials (n), the probability of success in each trial (p), and the number of successes (x). Additionally, the mean of a binomial distribution is equal to n*p, and the standard deviation is equal to √(n*p*(1-p)).

## 4. How is the binomial distribution used in real life?

The binomial distribution is used in various fields, including business, marketing, and social sciences, to model and analyze data that follows a binary outcome, such as success or failure, yes or no, etc. It is also used in hypothesis testing and decision-making processes.

## 5. Can the binomial distribution be approximated by a normal distribution?

Yes, the binomial distribution can be approximated by a normal distribution when the number of trials (n) is large (usually n ≥ 30) and the probability of success (p) is not too close to 0 or 1. This approximation is known as the central limit theorem.