# Approximation to the binomial distrubution

• Biochemgirl2002
In summary: Therefore, the standard deviation would be sqrt(npq) = sqrt(25*0.5*0.5) = 2.5. In summary, for a binomial random variable with n=50 trials and p=1/2, it is appropriate to use the normal approximation to the binomial distribution with a mean of 25 and a standard deviation of 2.5.
Biochemgirl2002
Homework Statement
Consider a binomial random variable with n = 50
trials and p = 1/2.
(A)Is it appropriate to use the normal
approximation to the binomial distribution? If so,
what mean and standard deviation we should we
use when standardizing?
Relevant Equations
X~N(mean, std dev^2)

X~N(np,npq) if np>5 and npq>5
a) since np has to be greater than 5,
n*p= 50*.5
=25
so yes, we can use this since it is much larger than 5.

now, for mean, i believe the equation is saying that the mean is np, which is 25
but in this equation we do not have a q value, so this is where my issue begins...
what should i use for my standard deviation?
do i square it once i find out what q is ?

rhiana said:
Homework Statement: Consider a binomial random variable with n = 50
trials and p = 1/2.
(A)Is it appropriate to use the normal
approximation to the binomial distribution? If so,
what mean and standard deviation we should we
use when standardizing?
Homework Equations: X~N(mean, std dev^2)

X~N(np,npq) if np>5 and npq>5

a) since np has to be greater than 5,
n*p= 50*.5
=25
so yes, we can use this since it is much larger than 5.

now, for mean, i believe the equation is saying that the mean is np, which is 25
but in this equation we do not have a q value, so this is where my issue begins...
what should i use for my standard deviation?
do i square it once i find out what q is ?
q is 1 - p, so for this situation, q = 1/2.

## 1. What is approximation to the binomial distribution?

Approximation to the binomial distribution is a statistical method used to estimate the probability of a certain number of successes in a fixed number of independent trials. It is based on the binomial distribution, which is a probability distribution that describes the likelihood of obtaining a certain number of successes in a fixed number of independent trials.

## 2. When is approximation to the binomial distribution used?

Approximation to the binomial distribution is typically used when the number of trials is large and the probability of success is small. In these cases, calculating the exact binomial probability may be time-consuming and difficult, so the approximation method is used as a simpler and more efficient alternative.

## 3. How is approximation to the binomial distribution calculated?

The approximation to the binomial distribution is calculated using the normal distribution. The mean and standard deviation of the normal distribution are calculated using the binomial distribution parameters (number of trials and probability of success), and then the desired probability is determined using the normal distribution formula.

## 4. What are the assumptions of approximation to the binomial distribution?

The main assumption of approximation to the binomial distribution is that the number of trials is large (typically at least 20) and the probability of success is small (typically less than 0.1). Additionally, the trials must be independent of each other and the probability of success must remain constant throughout all trials.

## 5. What are the advantages and disadvantages of using approximation to the binomial distribution?

The main advantage of using approximation to the binomial distribution is that it is a simpler and more efficient method compared to calculating the exact binomial probability, especially for large numbers of trials. However, the approximation method may not be as accurate as the exact calculation and is only applicable under certain assumptions, so caution should be taken when using it for data analysis.

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