A Teacher Finds That Final Grades in the Statistics Department $40 \% ; \mathrm { D } , 5 \% ; \mathrm { F } , 5 \%$

A teacher finds that final grades in the statistics department are distributed as: A, 25\%; B, 25\%; C, $40 \% ; \mathrm { D } , 5 \% ; \mathrm { F } , 5 \%$ . At the end of a randomly selected semester, the following grades were recorded. Calculate the chi-square test statistic $\chi ^ { 2 }$ used to determine if the grade distribution for the department is different than expected. Use $\alpha = 0.01$ .
$\begin{array}{l|lllll}\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 42 & 36 & 60 & 8 & 14\end{array}$

A) 6.87
B) 5.25
C) 3.41
D) 4.82