0Answer:
False. It applies mainly for the <em>Normal Distribution, </em>but not for <em>all</em> distributions.
Step-by-step explanation:
The empirical rule (known also as the 68-95-99.7 rule) is <em>particularly applied </em>to the <em>Normal Distribution</em> because of its unique characteristics such as its symmetry and definition by two parameters: the <em>mean</em> and the <em>standard deviation</em>.
That rule indicates that <em>below</em> and <em>above</em> the population's mean, within a distance of one standard deviation, there are 68.27% of the cases that follows this distribution; within two standard deviations, below and above, there are 95.45% of the values, and within three standard deviations 99.73% of the cases. <em>Not all distributions have this characteristic</em>.
Having into account such a characteristic, for populations that follow a Normal Distribution, we can standardize the values for this distribution using for this the <em>mean</em> and the <em>standard deviation</em>, ending up with a <em>standard normal distribution</em> in which this <em>empirical rule</em> is <em>true</em> for all data that follows a <em>normal distribution</em>. Because of this and that the Normal Distribution is symmetrical, we can determine probabilities for all populations that follow this distribution in a relatively easy way.
This can be achieved using the z-scores, that can be obtained using this formula:
Where <em>x</em> is a value for the population, is the population's mean and is the standard deviation, to then consulting a <em>standard normal table</em> to find the corresponding probabilities.