81. Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at Lucky claimed to wait in the checkout line until their turn. Let X = time in line. Table displays the ordered real data {in minutes}: 9.59 4.25 5 6 7.25 1.75 4.25 5.25 6 7.25 2 4.25 5.25 6.25 7.25 2.25 4.25 5.5 6.25 7.75 2.25 4.5 5.5 6.5 8 2.5 4.75 5.5 6.5 8.25 2.75 4.75 5.75 6.5 9.5 3.25 4.75 5.75 6.75 9.5 3.75 5 6 6.75 9.75 3.75 5 6 6.75 19.75 a) Calculate the sample mean and the sample standard deviation. b) Construct a histogram. c) Draw a smooth curve through the midpoints of the tops of the bars. d} In words, describe the shape of your histogram and smooth curve. e) Let the sample mean approximate p and the sample standard deviation approximate a. The distribution of X can then be approximated by X ~ ( , } f) Use the distribution in part e to calculate the probability that a person will wait fewer than 6.1 minutes. g) Determine the cumulative relative frequency for waiting less than 6.1 minutes. h) Why aren't the answers to part f and part g exactly the same? i) Why are the answers to part f and part g as close as they are? j) If only ten customers has been surveyed rather than 53, do you think the answers to part f and part g would have been closer together or farther apart? Explain your conclusion