Question: Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung conducted a survey as to how long customers at Lucky claimed to wait in the check out line until their turn. Let X= time in line. Below are the ordered real data (in minutes):

0.50 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 10.75

a. Calculate the sample mean and the sample standard deviation.

b. Construct a histogram. Start the x-axis at –0.375 and make bar widths of 2 minutes.

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 ??and the sample standard deviation approximate ???The distribution of X can then be approximated by X ~

f. Use the distribution in (e) to calculate 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 (f) and (g) exactly the same?

i. Why are the answers to(f) and (g) as close are they are?

j. If only 10 customers were survived instead of 50, do you think the answers to (f) and (g) would have been closer together or farther apart? Explain your conclusion.