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# Binomial Distribution and NC Army National Guard

In the military everything works of numbers. Recruiting is a good example of a binomial distribution. I'll use NC Army National Guard for an example.

The NCARNG must have a set number of enlistments every year and they get the requirement for the year during October.

This year the number is: 2000 (so n = 2000), the 2 out comes recruiters deal with are do they enlist or do they not enlist so we have a success if they enlist or a failure if they do not enlist (success or failure). This will give us a probability of success of 0.50 (p = .5).

Since everyone interviewed is a different person they are considered independent from each other.

The above distribution if looked at on a year to year base meets the requirements for a binomial distribution:

The requirements are listed below:

1. Each trial can have only two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure.

2. There must be a fixed number of trials.

3. The outcomes of each trial must be independent of each other.

4. The probability of a success must remain the same for each trial.

state how you would compute the mean and standard deviation for their distribution. Or if believe that the example does not meet all of the requirements for a binomial distribution, explain why.

#### Solution Preview

Mean is given by n*p = 2000*0.5 = 1000

Standard deviation = sqrt(n*p*q) = sqrt(2000*0.5*0.5) ...

#### Solution Summary

This solution uses the binomial distribution and calculates the mean and standard deviation of the trials. All steps are shown.

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