A Teacher Figures That Final Grades in the Statistics Department $$\chi _ { 0 } ^ { 2 }$$

A teacher figures 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 number of grades were recorded. Find the
Critical value χ $$\chi _ { 0 } ^ { 2 }$$ to determine if the grade distribution for the department is different than expected. Use $$\alpha =$$ .01. $$\begin{array} { l | l l l l l } \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 42 & 36 & 60 & 8 & 14\end{array}$$

A) 13.277
B) 11.143
C) 9.488
D) 7.779