In a College Dining Hall, Students with a Full Meal

Multiple Choice

In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution.Reviewing dining hall data over the past week, the following information is compiled. $$\begin{array} { | l | r | r | r | r | r | } \hline \text { Meals } & 0 & 1 & 2 & 3 & \geq 4 \\\hline \text { Observed frequency } & 287 & 581 & 447 & 290 & 185 \\\hline\end{array}$$ Using $\alpha$ =0.05, the critical value of chi-square for this goodness of fit test is _______.

A) 9.49
B) 7.81
C) 7.78
D) 10.28
E) 11.41