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A Multinomial Experiment With k=3k = 3 Cells And n=100n = 100

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A multinomial experiment with k=3k = 3 cells and n=100n = 100 has been conducted and the results are shown in the table.
 Cell 123ni463222\begin{array}{l}\quad\quad\text { Cell }\\\begin{array} { c | c c c } & 1 & 2 & 3 \\\hline n _ { i } & 46 & 32 & 22\end{array}\end{array}
Construct a 99% confidence interval for the multinomial probability associated with cell 2.

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