Consider an economy with two types of$$ firms, S and I. S firms all move together. I firms move independently. For both types of$$ firms, there is a $47\%$ probability that the firm will have a $13\%$ return and a $53\%$ probability that the firm will have a negative $15\%$ return. What is the volatility$($standard deviation$)$ of a portfolio that consists of an equal investment$$ in:

a$.38$ firms of type$$ S$?$

b$.38$ firms of type$$ I?