Samples of size n = 20 are randomly selected from 4 different bins of DVDs ranging in price from $4.99 to $9.99. You return each DVD before randomly drawing another and calculate the variance of each sample. What is the distribution of the sample variance?

We are given that, DVDs ranging in price from $4.99 to $9.99.

Therefore,

Range = Highest value - Lowest value = 9.99 - 4.99 = 5.

From this known value of Range, now we can find Standard deviation.

The range rule of thumb says that the

Standard deviation S = Range / 4.

Standard deviation S = 5 / 4 = 1.25.

Variance S^2 = 1.25^2 = 1.5625.

Now let us calculate the variance of each sample,

Sample Size = n = 20

standard deviation S = 1.25.

Standard deviation of the Sample = S / √n = 1.25 / √20 = 0.27951.

Variance of the Sample = 0.27951^2 = 0.078125.

What is the distribution of the sample variance?

The Sample variance S^2 follows Chi square distribution with degrees of freedom = n-1 = 20-1 = 19.

Chi square distribution is skewed to the right.