Use a ?² Test to Test the Claim That in the Given

Essay

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent
-An observed frequency distribution of exam scores is as follows: nging $\begin{array} { l| } \text { exam score}&under60&60-69&70-79&80-89&90-100\\\hline \text {frequncy }&30&30&140&60&40\\\end{array}$

i) Assuming a normal distribution with $\mu = 75$ and $\sigma = 15$ , find the probability of a randomly selected subject bel to each class. (Use boundaries of $59.5,69.5,79.5,89.5$ . )
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 $\sigma = 15$ .