Final answer:
The most suitable standard deviation for the provided distribution using the Empirical Rule appears to be 10, as this encompasses 95 percent of the values when considering two standard deviations from the mean, which is approximately 10 based on the symmetry of the data.
Step-by-step explanation:
Using the Empirical Rule and the provided distribution, we need to identify the standard deviation that best fits the data. The Empirical Rule is applicable only to distributions that are bell-shaped and symmetrical. It states that about 68 percent of data lies within one standard deviation of the mean, 95 percent within two standard deviations, and 99.7 percent within three standard deviations.
Let's start by looking for the mean of the distribution. Once we have the mean, we can apply the Empirical Rule to deduce the standard deviation. If the data were normally distributed, and given that the data looks symmetrically distributed around 10 (having an equal number of terms on either side), we could incrementally test standard deviations until we find one where approximately 95 percent of the data lies within two standard deviations of 10.
To find the standard deviation that matches the distribution, we would use the process of elimination based on the data points given. For example, if we select a standard deviation of 10, this would mean that 95 percent of our values would lie between -10 and 30, which encompasses all provided data points. Hence, this seems to be the correct standard deviation, since two standard deviations from the mean (10) cover almost all the provided data, adhering to the 95 percent rule of the Empirical Rule.