Question

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find the standard deviation.

Answer 1

`Sd(X) =√(1.2)=1.095`

Explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

`X \sim Binom(n=5, p=0.4)`

The probability mass function for the Binomial distribution is given as:

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

Where (nCx) means combinatory and it's given by this formula:

`nCx=(n!)/((n-x)! x!)`

The mean for the binomial distribution is given by:

`E(X) =np=5*0.4=2`

And the variance is given by:

`Var(X) = np(1-p) =5*0.4*(1-0.4)=1.2`

And the deviation is just the square root of the variance so we got:

`Sd(X) =√(1.2)=1.095`