It is claimed that the performance of the first year undergraduate students in Statistics course in one university can be studied in their ratios of grades. The ratios of distributions to grade $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are $3: 5: 2$ respectively. $\mathrm{A}$ total of 150 students are surveyed and the survey reveals the following result: \begin{tabular}{ICICCI) \hline Grade A & Grade B & Grade C W Vhline 51 & 81 & 18 \hline \end{tabular) (a) If the null hypothesis $(3: 5: 2)$ is true, detemine the expected number of students that score A, B and C respectively in Statistics? (b) Complete the hypothesis test using the $0.01$ significance level. SP.SD.047