The author claims that his fit is: sick_hours = -52 * ln(x) + 236, not sick days. Furthermore, your conclusion should read p = 1 - exp(- sick_hours/52)

The author claims that his fit is: sick_hours = -52 * ln(x) + 236, not sick days. Furthermore, your conclusion should read p = 1 - exp(- sick_hours/52). Then, the units in the exp() cancel and everyone is happy. But I assume that's what you meant by stating lambda=1/52.