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 $49\%$ probability that the firm will have a $17\%$ return and a $51\%$ probability that the firm will have a negative $3\%$ return. What is the volatility$($standard deviation$)$ of a portfolio that consists of an equal investment$$ in:

a$.32$ firms of type$$ S$?$

b$.32$ firms of type$$ I?

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Part $1$

a$.$ What is the volatility$($standard deviation$)$ of a portfolio that consists of an equal investment in $32$ firms of type$$ S$?$

Standard deviation is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $2$

b$.$ What is the volatility$($standard deviation$)$ of a portfolio that consists of an equal investment in $32$ firms of type$$ I?

Standard deviation is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$