Biosyn said:Homework Statement
Find the value of Ʃn(18 n)(0.46)^2(0.54)^(18-n)
The sum is from n = 0 to n=18
Sorry, I do not know how to format it.
Homework Equations
I am using the Binomial Expansion Theorem:
The Attempt at a Solution
Not sure where to start.
P = 0.46
Q = 0.54
n = 18
k = ?
The Binomial Distribution is a probability distribution that describes the number of successes in a series of independent trials with two possible outcomes, such as success or failure. It is often used to model the probability of obtaining a certain number of successes in a fixed number of trials.
The Binomial Distribution has two parameters: n, the number of trials, and p, the probability of success in each trial. The number of successes, k, can range from 0 to n.
The Binomial Distribution is a discrete probability distribution, while the Normal Distribution is a continuous probability distribution. This means that the Binomial Distribution only applies to situations where the outcomes are discrete (such as success or failure), while the Normal Distribution can be used for any continuous variable.
The mean of the Binomial Distribution is given by np, and the standard deviation is given by sqrt(np(1-p)). This means that as the number of trials increases, the mean and standard deviation also increase, making the distribution more spread out.
The Binomial Distribution is used in many real-life scenarios, such as in quality control to determine the probability of a certain number of defective products in a batch, in genetics to model the probability of inheriting a particular trait, and in finance to calculate the likelihood of a certain number of successful investments. It is also commonly used in hypothesis testing and statistical inference.