The Number of Contaminating Particles on a Silicon Wafer Prior

Essay

The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample size 100, resulting in the following frequencies: $\begin{array}{cccc}\hline \text { Number of particles } & \text { Frequency } & \text { Number of particles } & \text { Frequency } \\\hline 0 & 1 & 8 & 12 \\\hline 1 & 2 & 9 & 4 \\\hline 2 & 3 & 10 & 5 \\\hline 3 & 12 & 11 & 3 \\\hline 4 & 11 & 12 & 1 \\\hline 5 & 15 & 13 & 2 \\\hline 6 & 18 & 14 & 1 \\\hline 7 & 10 & &\\\hline \end{array}$

a. What proportion of the sampled wafers had at least two particles? At least six particles?
b. What proportion of the sampled wafers had between four and nine particles, inclusive? Strictly between four and nine particles?