A Teacher Figures That Final Grades in the Chemistry Department $\mathrm { A } , 25 \% ; \mathrm { B } , 25 \% ; \mathrm { C } , 40 \% ;$

Multiple Choice

A teacher figures that final grades in the chemistry department are distributed as: $\mathrm { A } , 25 \% ; \mathrm { B } , 25 \% ; \mathrm { C } , 40 \% ;$ D, $5 \% ;$ F, $5 \%$ . At the end of a randomly selected semester, the following number of grades were recorded. Find the critical value $\chi _ { 0 } ^ { 2 }$ 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) $13.277$
B) $15.086$
C) $9.488$
D) $7.779$