If we were tasked to reach various conclusions based on such data, how would we structure our models? This article sets to answer these questions. To begin this study, we will review a series of example problems.

**Example 1:**

The military has instituted a new training regime in order to screen candidates for a newly formed battalion. Due to the specialization of this unit, candidates are vetted through exercises which screen through the utilization of extremely rigorous physical routines. Presently, only 60% of candidates who have attempted the regime, have successfully passed. If 100 new candidates volunteer for the unit, what is the probability that more than 70% of those candidates will pass the physical?

**# Disable Scientific Notation in R Output #**

options(scipen = 999)

**# Find The Standard Deviation of The Sample #**

**sqrt(.4 * .6/ 100)**

*[1]*

*0.04898979*

**# Find the Z-Score #**

**(.7 - .6)/0.04898979**

*[1] 2.041242*

Probability of Z-Score 2.041242 = .4793

(Check Z-Table)

Finally, conclude as to whether the probability of the sample exceeds 70%

(One tailed test)

**.50 - .4793**

*[1] 0.0207*

In R, the following code can be used to expedite the process:

**sqrt(.4 * .6/ 100)**

*[1] 0.04898979*

**pnorm(q=.7, mean=.6, sd=0.04898979 , lower.tail=FALSE)**

*[1] 0.02061341*

So, we can conclude, that if 100 new candidates volunteer for the unit, there is only a 2.06% chance that more than 70% of those candidates will pass the physical.

The process really is that simple.

In the next article we will review confidence interval estimate of proportions.

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