1. Consider the following questions concerning the sample variance:
a. Is it possible for a variance to be negative? Explain.
b. What is the smallest value a variance can be? Under what conditions does the variance equal this smallest value?
c. Under what conditions is the sample variance smaller than the corresponding sample standard deviation?
2. For a continuous variable that has a bell-shaped distribution, determine the percentiles associated with the endpoints of the intervals specified in the Empirical Rule.
3. Consider that the Empirical Rule stipulates that virtually all of the data values are within the interval m 3s. Use this stipulation to determine an approximation for the standard deviation involving the range.