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 6.1 displays the ordered real data (in minutes):

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 μ and the sample standard deviation approximate σ. 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 50, do you think the answers to part f and part g would have been closer together or farther apart? Explain your conclusion.

Transcribed Image Text:

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 Table 6.1