The U.S. Census Bureau (2000 census) reported the following relative frequency distribution for travel time to work for a large sample of adults who did not work at home:
|
Travel Time
(minutes)
|
Relative Frequency
|
|
0 to 5
|
.04
|
|
5 to 10
|
.13
|
|
10 to 15
|
.16
|
|
15 to 20
|
.17
|
|
20 to 25
|
.14
|
|
25 to 30
|
.05
|
|
30 to 35
|
.12
|
35 to 40 .03
40 to 45 .03
45 to 60 .06
60 to 90 .05
90 or more .02
a. Draw the histogram for the travel time distribution. In constructing the histogram, assume that the last interval in the relative frequency distribution (90 or more) ends at 200; so the last interval is 90 to 200. Be sure to use the density scale to determine the heights of the bars in the histogram because not all the intervals have the same width.
b. Describe the interesting features of the histogram from Part (a), including center, shape, and spread.
c. Based on the histogram from Part (a), would it be appropriate to use the Empirical Rule to make statements about the travel time distribution? Explain why or why not.
d. The approximate mean and standard deviation for the travel time distribution are 27 minutes and 24 minutes, respectively. Based on this mean and standard deviation and the fact that travel time cannot be negative, explain why the travel time distribution could not be well approximated by a normal curve.
e. Use the mean and standard deviation given in Part
(d) and Chebyshev's Rule to make a statement about
i. the percentage of travel times that were between 0 and 75 minutes
ii. the percentage of travel times that were between 0 and 47 minutes
f. How well do the statements in Part (e) based on Chebyshev's Rule agree with the actual percentages for the travel time distribution? (Hint: You can estimate the actual percentages from the given relative frequency distribution.)