A Teacher Finds That Final Grades in the Statistics Department $40 \%$

Multiple Choice

A teacher finds that final grades in the statistics department are distributed as: A, 25\%; B, 25\%; C, $40 \%$ ; 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 $\alpha = 0.01$ .
$\begin{array}{l|ccccc}\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 42 & 36 & 60 & 14 & 8\end{array}$

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