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 $\sigma = 15$.

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The Answer of 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 $\sigma = 15$.

An Observed Frequency Distribution of Exam Scores Is as Follows