Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows: Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210

Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?