A Multinomial Experiment With $k = 4$ Cells And $n = 400$

Multiple Choice

A multinomial experiment with $k = 4$ cells and $n = 400$ produced the data shown in the following table.
$\begin{array} { r | r c c r } &\text { Cell }\\& 1 & 2 & 3 & 4 \\\hline n _ { i } & 50 & 213 & 104 & 33\end{array}$

Previous studies in this area have shown that $p _ { 1 } = p _ { 2 } = p _ { 3 } = p _ { 4 } = .25$ . Construct a $95 \%$ confidence interval for the multinomial probability associated with cell 2

A) (0.491, 0.574)
B) (0.490, 0.575)
C) (0.093, 0.157)
D) (0.484, 0.581)