An Observed Frequency Distribution of Exam Scores Is as Follows

Essay

An observed frequency distribution of exam scores is as follows: $\begin{array}{l|ccccc}\text { Exam Score } & \text { Under } 60 & 60-69 & 70-79 & 80-89 & 90-100 \\\hline \text { Frequency } & 30 & 30 & 140 & 60 & 40\end{array}$
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 $\sigma = 15$ .