According to the website http://www.digitalbookworld.com, the average price of a bestselling ebook increased to \(\$ 8.05\) in the week of February 18, 2015, from \(\$ 6.89\) in the previous week. Assume the standard deviation of the price of a bestselling ebook is \(\$ 1\), and suppose you have a sample of 20 bestselling ebooks with a sample mean of \(\$ 7.80\) and a standard deviation of \(\$ 0.95\).

a. Identify the random variable \(X\) in this study. Indicate whether it is quantitative or categorical.

b. Describe the center and variability of the population distribution. What would you predict as the shape of the population distribution? Explain.

c. Describe the center and variability of the data distribution. What would you predict as the shape of the data distribution? Explain.

d. Describe the center and variability of the sampling distribution of the sample mean for 20 bestselling ebooks. What would you predict as the shape of the sampling distribution? Explain.