Question

What is the formula for the standard deviation of a binomial distribution?

Answer 1

Hint: The binomial distribution is a process with two possible outcomes i.e. success or failure. Standard deviation of a binomial distribution is the square root of variance of binomial distribution. By using this concept we will get the desired answer.

Complete step by step solution:
We have to find the formula for the standard deviation of a binomial distribution.
We know that the binomial distribution is a process with two possible outcomes i.e. success or failure and definite number of trials. The probability of outcomes of a binomial distribution is denoted by p and q, where p is the probability of success and q is the probability of failure. If n denotes the number of trials then the relationship between p and q is defined as
$\Rightarrow q=1-p$
Now, the standard deviation of a binomial distribution is given by the formula
$= \sqrt{np\left( 1-p \right)}$
When we substitute the value of q we will get
$= \sqrt{npq}$
Hence above is the required formula for the standard deviation of a binomial distribution.

Note: The point to be noted is that in binomial distribution the values of p and q cannot be negative because both are probabilities and probability cannot be negative. The binomial distribution is performed several times but the value of n is definite. We can also find the deviation by taking the square root of variance.