An Observed Frequency Distribution of Exam Scores Is as Follows $\begin{array} { l| } \text {Exam Score }& \text {under 60 }&60-69&70-79&80-89&90-100\\ \hline \text {Frequency }&36&75&85&70&34\end{array}$

Essay

An observed frequency distribution of exam scores is as follows: $\begin{array} { l| } \text {Exam Score }& \text {under 60 }&60-69&70-79&80-89&90-100\\ \hline \text {Frequency }&36&75&85&70&34\end{array}$

i) Assuming a normal distribution with $\mu = 75$ and $\sigma = 15$ , find the probability of a randomly selected subject belonging to each class. (Use boundaries of $59.5,69.5,79.5,89.5$ , 100.)
ii) Using the probabilities found in part (i), find the expected frequency for each category.
iii) Use a $0.05$ significance level to test the claim that the exam scores were randomly selected from a normally distributed population with $\mu = 75$ and $\sigma = 15$ .