Final answer:
In a normally distributed variable, virtually all observed values should be between μ + 3σ and μ - 3σ, according to the Empirical Rule, which states that this range encompasses about 99.7 percent of the data points.
Step-by-step explanation:
If a process variable is normally distributed, in the long run, virtually all observed values should be between μ + 3σ and μ - 3σ. This range encompasses about 99.7 percent of the data points according to the Empirical Rule, which is a statistical rule stating the proportion of values that fall within certain standard deviations from the mean in a normal distribution.
The z-scores are also related to this rule. For example:The Empirical Rule states that if a process variable is normally distributed, in the long run virtually all observed values should be between μ - 3σ and μ + 3σ. This means that there is a 99.7 percent chance that the values will fall within three standard deviations of the mean.For example, if the mean is 50 and the standard deviation is 6, then virtually all observed values should be between 32 and 68.The answer is option A) μ + 3σ and μ - 3σ.Hence, the correct answer to the question is Option A) μ + 3σ and μ - 3σ.