A Biology Professor Claims That, on the Average $15 \%$ Of Her Students Get a Grade of A

A biology professor claims that, on the average, $15 \%$ of her students get a grade of A, $25 \%$ get a B, $40 \%$ get a C, $15 \%$ get a D, and $5 \%$ get an F. The grades of a random sample of 115 students were recorded. The following table presents the re
$\begin{array}{c|lllll}\text { Grade } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 28 & 24 & 39 & 17 & 7\end{array}$

i). Compute the expected frequencies.
ii). What is the value of $\chi ^ { 2 }$ ?
iii). How many degrees of freedom are there?
iv). Test the hypothesis that the grades follow the distribution claimed by the profi Use the $\alpha = 0.01$ level of significance.