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.
