Chapter 3.3, Problem 31E

Use the commute time data given in the previous exercise to complete the following:

1. a. Calculate the cumulative relative frequencies, and construct a cumulative relative frequency plot.
2. b. Use the cumulative relative frequency plot constructed in Part (a) to answer the following questions.
   1. i. Approximately what proportion of commute times were less than 50 minutes?
   2. ii. Approximately what proportion of commute times were greater than 22 minutes?
   3. iii. What is the approximate commute time value that separates the shortest 50% of commute times from the longest 50%?

3.30 U.S. Census data for San Luis Obispo County, California, were used to construct the following relative frequency distribution for commute time (in minutes) of working adults in 2015 (datausa.io/profile/geo/san-luis-bispo-paso-robles-ca-metro-area/#housing, retrieved February 18, 2018) and so are only approximate):

1. a. Notice that not all intervals in the frequency distribution are equal in width. Why do you think that unequal width intervals were used?
2. b. Construct a table that adds a density column to the given relative frequency distribution. (Hint: See Example 3.17.)
3. c. Use the densities computed in Part (b) to construct a histogram for this data set. (The web site referenced earlier actually displays an incorrectly drawn histogram based on relative frequencies rather than densities!) Write a few sentences commenting on the important features of the histogram.