When sampling from a population (in this case, bins of DVDs with prices) and calculating the sample variance, the distribution of the sample variance can be influenced by the underlying distribution of the data.
Since the prices of the DVDs are continuous and can vary between $4.99 and $9.99, if we assume that the prices are uniformly distributed across this range, the sample variance will also tend to be relatively uniform, especially for small sample sizes. However, the question does not specify the underlying distribution of prices, nor does it provide enough information to assume a specific distribution.
Generally, the distribution of the sample variance (s²), given a normal population, follows a chi-squared distribution. But if the population is not normally distributed, the distribution of the sample variance can be right-skewed.
Given the nature of the problem (sampling from a finite range of values without specifying the distribution) and small sample size, we cannot definitively state the distribution shape.
However, since the sample variance is influenced by the underlying data variability, and considering the potential for variability in real-world data, the most likely answer is:
• distribution skewed to the right
This choice acknowledges the reality that sample variances can be positively skewed, particularly when the underlying prices are bounded and potentially cluster around a specific range.