A Teacher Finds That Final Grades in the Statistics Department $\mathrm { A } , 25 \% ; \mathrm { B } , 25 \% ; \mathrm { C } , 40 \% ; \mathrm { D } , 5 \%$

A teacher finds that final grades in the statistics department are distributed as: $\mathrm { A } , 25 \% ; \mathrm { B } , 25 \% ; \mathrm { C } , 40 \% ; \mathrm { D } , 5 \%$ ; 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 $\alpha = 0.01$

$\begin{array}{l|lllll}\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 36 & 42 & 60 & 14 & 8\end{array}$

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