An Observed Frequency Distribution of Exam Scores Is as Follows

Essay

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


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 $\sigma = 15$ .