# What Is the 95 Percent Rule in Statistics

De Moivre discovered rule 68 95 99.7 with an experiment. You can make your own experience by launching 100 fair trade coins. Note: In particular, the rule of thumb predicts that 68% of observations are in the first standard deviation (μ ± σ), 95% in the first two standard deviations (μ ± 2σ) and 99.7% in the first three standard deviations (μ ± 3σ). The percentage of data composing the 2nd and 3rd AND 3rd DT is 13.5% + 2.35% = 15.85% 68-95-99.7 Rule: another name for the rule of thumb To understand where the percentages come from, it is important to know the probability density function (PDF). A PDF file is used to specify the probability that the random variable will fall within a certain range of values instead of taking a value. This probability is given by the integral pdf file of this variable over this range – that is, it is given by the area under the density function, but above the horizontal axis and between the lowest and largest value in the range. This definition may not make much sense, so let`s clarify it by graphically representing the probability density function for a normal distribution. The following equation is the probability density function for a normal distribution If the price per pound of USDA Choice beef is typically distributed with an average of \$4.85/lb and a standard deviation of \$0.35/lb, what is the estimated probability that a randomly selected sample (from a randomly selected market) is between \$5.20 and \$5.55 per pound? The rule of thumb is applied to anticipate likely outcomes in a normal distribution. For example, a statistician would use it to estimate the percentage of cases that fall within each standard deviation. Note that the standard deviation is 3.1 and the mean is 10.

In this case, the first standard deviation would be between (10+3.2)= 13.2 and (10-3.2)= 6.8. The second gap would be between 10 + (2 X 3.2) = 16.4 and 10 – (2 X 3.2) = 3.6, etc. You can also use z-scores to calculate probabilities and percentiles of data that follow the normal distribution. For more information, see my article Z-Score: Definition, Formula, and Uses. Use the same process for the other rule of thumb percentages using multiples 2X and 3X of the standard deviation. 95% have between 20 and 40 minutes (30 +/- 2 * 5) and 99.7% between 15 and 45 minutes (30 +/-3 * 5). The following diagram graphically illustrates this property. The integral can be evaluated for standard deviations in order to derive the rule of thumb: at 68%, the approximation of the rule of thumb is quite close: Can you use the rule of thumb to determine how to determine the probability of a delivery between 35-40 minutes? Let`s work on an example problem for the rule of thumb. Suppose a pizzeria has an average delivery time of 30 minutes and a standard deviation of 5 minutes, and the data follows the normal distribution. The rule of thumb is often used in statistics to predict final outcomes. After calculating the standard deviation and before collecting accurate data, this rule can be used as a rough estimate of the outcome of the pending data to be collected and analyzed.

The rule of thumb calculator (also a 68 95 99 rule calculator) is a tool for finding the ranges that are 1 standard deviation, 2 standard deviations and 3 standard deviations from the mean, in which you will find respectively 68, 95 and 99.7% of the normally distributed data. In the following text, you will find the definition of the rule of thumb, the formula of the rule of thumb and an example of how to use the rule of thumb. From Chebyzhov`s inequality, a weaker three sigma rule can be derived, which states that even for non-normally distributed variables, at least 88.8% of cases should fall within correctly calculated three sigma intervals. For unimodal distributions, the probability of being in the interval is at least 95% due to the Vysochanskij-Petunin inequality. There may be certain assumptions for a distribution that force this probability to be at least 98%.  You can use the rule if you are told that your data is normal or close to normal, or if you have a unimodal distribution (i.e. with a single peak) that is symmetrical. If a question mentions a normal or near-normal distribution and you get standard deviations, it almost certainly means that you can use the rule to determine approximately how many of your values fall within a certain number of standard deviations.

As an analyst using the rule of thumb, you must distinguish between outliers and non-normal distributions. Both conditions can result in an unusual number of data points outside the three sigma limit. For example, observations may be valid but follow a distorted distribution that may give the appearance of outliers. To sort through this question, you need to carefully evaluate your data, determine how it is distributed, evaluate the data points in question, and apply a large amount of expertise. Rule 68 95 99.7 was first invented by Abraham de Moivre in 1733, 75 years before the publication of the normal distribution model. De Moivre worked in the field of probability development. Perhaps his greatest contribution to statistics was the 1756 edition of The Doctrine of Chances, which included his work on the approach of the binomial distribution by the normal distribution in the case of a large number of attempts. The exponential function e-z2/2 has no simple anti-derivative, so the integral must be calculated with numerical integration. For example, as a Taylor series or with Riemann sums (Simpson`s rule is one of the best variants).

The person who solves this problem must calculate the overall probability that the animal will live 14.6 years or more. The rule of thumb shows that 68% of the distribution is within a standard deviation, in this case 11.6 to 14.6 years. Thus, the remaining 32% of the distribution is outside this range. One half is greater than 14.6 and the other half is less than 11.6. Thus, the probability that the animal will live more than 14.6 years is 16% (calculated as 32% divided by two). Because of the probabilities associated with the 1, 2, and 3 SDs, the rule of thumb is also known as the 68−95−99.7 rule. This is related to the confidence interval as used in statistics: X ̄ ± 2 σ n {displaystyle {bar {X}}pm 2{frac {sigma }{sqrt {n}}}} is approximately a 95% confidence interval if X ̄ {displaystyle {bar {X}}} is the average of a sample of size n {displaystyle n}. . . .

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