The empirical rule states that for normal distribution nearly all data will fall into one of

three deviations of the mean. I took on the topic of boys and their voices getting lower and

or deeper for an example. Boys ages where their voices get deeper have to get distributed

normally so it fits in the category. The average age for a boys voice to lower and or get

deeper is thirteen with deviation of one point two years. This follows the empirical rule

because were on topic of normal age the boys get their depend and or lowered voices when

they reach around thirteen years of age. There are some who get it before thirteen years of

age and some who get it after the age of thirteen. First deviation, sixty eight percent and is

the ages eleven point eight to fourteen point two. Second deviation, is ninety five percent

and is the ages ten point six to fifteen point four. The third and final deviation is ninety

nine percent and is between the ages nine point four and sixteen point six. My research into

the NBA player heights revealed a mean height of 79 inches with a standard deviation of

3.5 inches, forming a roughly normal bell-shaped curve. The tallest player had a height of

91 inches. Using the 68-95-99.7 rule as applied to this situation means that 68% of players

fell within one standard deviation of the mean. Specifically, 68% of players had heights

between 75.5 and 82.5 inches. Likewise, the second standard deviation included 95% of

players that had heights between 72 inches and 86 inches. The third standard deviation

represented 99.7% of players that had heights between 68.5 inches and 89.5 inches. I

believe this data to be true because the the tallest player is so close to the third standard

deviation. He would represent the tallest 0.15%. As we know, there must be a tallest player

and a shortest player. Combined, they account for 0.30% of the population. Based on the

sample size, 0.30% equates to 2 people: one is the tallest player and one is the shortest

player. In this respect, the distribution curve appears to reflect accurately. The empirical

rule can be used to find the normal distribution of the heights of women to follow a bell-

shaped distribution with a mean of 160cm, and a standard deviation of 7.5cm.

In this example we are trying to find out what the approximate percentage of women

between 137.5cm and 182.5cm are.

To find the empirical rule in this example, first you find the number of standard deviations

by finding the mean of 160 and multiply it by 7.5, which equals 182.5, then you add to k

by subtracting 160 by both sides, lastly you divide both sides by 3, and there are 3 standard

deviations. Using the empirical rule, the approximate percentage of the woman's height

between 137.5cm and 182.5cm averages 99.7%

The margin of error considers the z score associated with the confidence interval and the

standard error. The standard error indicates the standard deviation in the population of all

possible means (or proportions) drawn from the population.

Also known as three sigma rule or 68-95-99-7 rule. Statistical rule states that a normal

distribution observes data which almost falls within the three standard deviation of the

mean, or average.

In particular, the empirical rule predicts that 68% of observations falls within the first

standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and

99.7% within the first three standard deviations (µ ± 3σ).

Empirical research can be conducted and analyzed using qualitative or quantitative methods.

• Quantitative research: Quantitative research methods are used to gather

information through numerical data. It is used to quantify opinions, behaviors or

other defined variables. These are predetermined and are in a more structured

format. Some of the commonly used methods are survey, longitudinal studies, polls,

etc.

• Qualitative research: Qualitative research methods are used to gather non

numerical data. It is used to find meanings, opinions, or the underlying reasons from

its subjects. These methods are unstructured or semi structured. The sample size for

such a research is usually small and it is a conversational type of method to provide

more insight or in-depth information about the problem Some of the most popular

forms of methods are focus groups, experiments, interviews, etc.

Data collected from these will need to be analyzed. Empirical evidence can also be

analyzed either quantitatively and qualitatively. Using this, the researcher can answer

empirical questions which have to be clearly defined and answerable with the findings he

has got. The type of research design used will vary depending on the field in which it is

going to be used. Many of them might choose to do a collective research involving

quantitative and qualitative method to better answer questions which cannot be studied in a

laboratory setting.

Let’s say the population size of wild animals in a zoo is said to be normally distributed.

On an average, one animal has a lifespan of 13.1 years, and the standard deviation is 1.5

years. For determining the probability of a wild animal living more than 14.6 years, one

can consider using the empirical rule. As mentioned earlier, the average of distribution

being 13.1 years, there will be following age ranges determined for every standard

deviation.” (Gordon, 2021).

The empirical rule is used to predict the final results in statistics. This means that an

estimation will exist between the two standard deviations of the mean. The empirical rule

would be used in this scenario to figure out the probability of an animal in the zoo of living

at least 14.6 years. This example gives clear numbers to base the probability theory off of.

Following the trends and patterns of the animals life spans within the zoo could make a

great comparison to each other in order to find out a number. Not every example is easy.

An example of how the Empirical Rule works within my organization, I leveraged both

Investopedia.com and Images found on Google to ensure my understanding was mostly on

point; showing myself grace if not, as this is new for most if not all of us. My takeaway is

that a call center can take data based on historical data to assess how many team members

take a percentage of calls each day. From this analysis it can be determined that X number

of calls are managed by a single person each day, and a standard deviation can be

considered. An analyst is then able to leverage the Empirical Rule to further breakdown the

analysis and identifying the best approach for the company. A situation in which the

empirical rule can be applied would be measuring heights of people. You can choose a

sample set of people and get all of their heights in inches and gather all the data. Typically,

you will have some shorter, majority average height and then some taller which would

follow a normal distribution. However, when graphed, you can see that more than likely, it

will be a bell shaped curve with majority of people falling into an average height category.

This follows the empirical rule because each set will fall into a different deviation whether

one, two or three standard deviations. With this example you would need to select a diverse

population and not all from specific areas who would have identical/similar heights.

Analysts use the empirical rule to predict the probabilities and distributions of the outcomes

they are studying. This rule also helps determine what outliers are within the data captured.

The mean and the standard deviation are valuable pieces of data since it allows to calculate

the probabilities and percentages for various outcomes. Upon my research to determine

ways the Empirical Rule I discovered a site that showed the graph for Distribution of Pizza

Delivery Times. Per the page Statistics by Jim "A pizza restaurant has a mean delivery time

of 30 minutes and a standard deviation of 5 minutes" This information provides the

employer with how long it is taking the customers to receive their pizza. It also can help

the employer determine which of their employees are delivering pizzas in a timely matter

and which ones are not being as productive. In statistics, the empirical rule is used for the

purpose of forecasting the final outcome. After the calculation of the standard deviation and

prior to collecting the exact data, the empirical rule can be used to arrive at a rough

estimate of the outcome of the impending data for collection and analysis. The use of the

probability distribution is considered important as it can be used as interim heuristic

(Artyushenko et al., 2020). A situation in which the data that is collected for representing

the situation follows a normal distribution involves three students playing basketball, out of

which one of them is a good player, one of them is an average player, and the third one

does not know how to play the sport (Artyushenko et al., 2020). In the specific situation,

the good player is likely to make the most score, whereas the average player is likely to

make a few shots while playing the game. On the other hand, the student who does not

know how to play basketball may not be able to play it at all. The situation follows

empirical rue since there is a normal distribution of the game scores. The key benefit that

may exist because the situation has data that is distributed normally is that probability can

be ascertained from the information. During the recent election season, you saw many

instances where polls were taken and reported, along with the confidence level of the

estimate. For example, a poll showed that one candidate had a ""voting for" level of 37%+/-

4. The opposing candidate had a score of 39%+/-4 at a 95% confidence level. Because the

poll is not a census sample, a sample may be "good" but will have variation around the

TRUE population proportion or mean. Thus, the poll is an estimate. The +/- value

establishes a range within which the true population proportion is said to be, given a certain

level of confidence. The empirical rule is when pieces of data will fall within 3 standard

deviations of the mean in a normal data set. It is also referred to the 3 sigma rule “68-95-

99.7 rule”. The reason for this is the first standard deviation from the mean, 68% of data

rests, 95% of data will fall within the 2 standard deviation, and nearly 99.7% of all data

falls within the 3 standard deviations. This rule can be useful for forecasting final outcomes

within a data set.

A situation where you can collect data and the empirical rule applies is finding the

probability that an average animal at the zoo will live longer than 14.6 years. The

distribution means is 13.1 years old and standard deviation lifespan is 1.5 years.

• Thefirst standard deviation 13.1-1.5 to 13.1 + 1.5 or 11.6 to 14.6.

• Twostandard deviation 13.1- (2 x 1.5) to 13.1 + (2 x 1.5), or 10.1 to 16.1

• Threestandard deviations 13.1 - (3 x 1.5) to 13.1 + (3 x 1.5), or, 8.6 to 17.6

The probability of the animal living for more than 14.6 years is 16% because the remaining

32% of the distribution is outside the range. One half is above the range of 14.6 and the

other below 11.6.

In statistics, the empirical rule states that 99.7% of data occurs within three standard

deviations of the mean within a normal distribution. To this end, 68% of the observed data

will occur within the first standard deviation, 95% will take place in the second deviation,

and 97.5% within the third standard deviation. The empirical rule predicts the probability

distribution for a set of outcomes. f

The empirical rule is applied to anticipate probable outcomes in a normal distribution. For

instance, a statistician would use this to estimate the percentage of cases that fall in each

standard deviation. Consider that the standard deviation is 3.1 and the mean equals 10. In

this case, the first standard deviation would range between (10+3.2)= 13.2 and (10-3.2)=

6.8. The second deviation would fall between 10 + (2 X 3.2)= 16.4 and 10 - (2 X 3.2)=

3.6, and so forth. Now, on a personal note, this looks like my retirement plan. Seriously,

when I go on my retirement plans (401k and define benefit), those formulas look exactly

like, how I am supposed to retire. I put in a certain percentage in my 401k, my employer

matches, and then with the define benefit (pension employer contribution) it is on top

meaning with minimal loss. My 401K, fluctuate with distributions and the stock market

plays a key role into it as well.My retirement can go up, rest, and fall (bell curve). The

way I am paid is by a percentage, and if I work more one week than the other, my

distributions differ. Next, if the stock market and my bonds go up, my retirement goes up,

then, it can just rest. Meaning, if no change is in the market so everything sits at the top

of the bell. The real tick off, and I do apologize class for the term, for as my personal life,

inflation, the price of food, gasoline, energy, natural gas, and my stress level from all of

this.