Questions: Question 1.12: 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 a) What proportion of the observations are less than 5 ?

Solution Steps

To determine the total number of observations, we sum the frequencies of all particle size intervals:

\[ \text{Total Observations} = 5 + 15 + 27 + 34 + 22 + 14 + 7 + 2 + 4 + 1 = 131 \]

Next, we calculate the number of observations that fall within the intervals less than 5 nm, which are \(3.0-<3.5\), \(3.5-<4.0\), and \(4.0-<4.5\):

\[ \text{Observations Less Than 5} = 5 + 15 + 27 = 47 \]

Now, we find the proportion of observations that are less than 5 nm by dividing the number of observations less than 5 by the total number of observations:

\[ \text{Proportion Less Than 5} = \frac{\text{Observations Less Than 5}}{\text{Total Observations}} = \frac{47}{131} \approx 0.36 \]

Final Answer