Chapter 1.2, Problem 12E

The accompanying summary data on CeO₂ particle sizes (nm) under certain experimental conditions was read from a graph in the article “Nanoceria-Energetics of Surfaces, Interfaces and Water Adsorption” (J. of the Amer. Ceramic Soc., 2011: 3992-3999):

3.0−<3.5	3.5−<4.0	4.0−<4.5	4.5−<5.0	5.0−<5.5
5	15	27	34	22
5.5−<6.0	6.0−<6.5	6.5−<7.0	7.0−<7.5	7.5−<8.0
14	7	2	4	1

1. a. What proportion of the observations are less than 5?
2. b. What proportion of the observations are at least 6?
3. c. Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed? [Note: The investigators fit a lognormal distribution to the data; this is discussed in Chapter 4.]
4. d. Construct a histogram with density on the vertical axis and compare to the histogram in (c).