Solve all with excel formular format: $1.$ You are managing a portfolio consisting of two stocks: Stock A and Stock B$.$ Stock A has an average yearly return of $15\%$ with a standard deviation of $10\%,$ while Stock B has an average yearly return of $10\%$ with a standard deviation of $5\%.$ The correlation between the returns of Stock A and Stock B is $0\mathrm{.}6.$ What is the probability that the portfolio return, defined as $0\mathrm{.}6*$Stock A $+0\mathrm{.}4*$Stock B$,$ exceeds $12\%?$

$2.$ Suppose you have investments in two different funds: Fund X and Fund Y$.$ Fund X has an average annual return of $8\%$ with a standard deviation of $12\%,$ while Fund Y has an average annual return of $12\%$ with a standard deviation of $18\%.$ The correlation between the returns of Fund X and Fund Y is $0\mathrm{.}3.$ Calculate the probability that the portfolio return, defined as $0\mathrm{.}7*$Fund X $+0\mathrm{.}3*$Fund Y$,$ is less than $10\%.$

$3.$ You are considering investing in two bonds: Bond P and Bond Q$.$ Bond P has an average yearly return of $6\%$ with a standard deviation of $3\%,$ while Bond Q has an average yearly return of $8\%$ with a standard deviation of $5\%.$ The correlation between the returns of Bond P and Bond Q is $-0\mathrm{.}2.$ Determine the probability that the portfolio return, defined as $0\mathrm{.}4*$Bond P $+0\mathrm{.}6*$Bond Q$,$ is greater than $7\%.$

$4.$ You are managing a portfolio comprising two assets: Asset X and Asset Y$.$ Asset X has an average annual return of $12\%$ with a standard deviation of $8\%,$ while Asset Y has an average annual return of $10\%$ with a standard deviation of $6\%.$ The correlation between the returns of Asset X and Asset Y is $0\mathrm{.}5.$ Find the probability that the portfolio return, defined as $0\mathrm{.}6*$Asset X $+0\mathrm{.}4*$Asset Y$,$ exceeds $11\%.$

$5.$ Consider a portfolio consisting of two investment options: Option A and Option B$.$ Option A has an average yearly return of $18\%$ with a standard deviation of $15\%,$ while Option B has an average yearly return of $10\%$ with a standard deviation of $8\%.$ The correlation between the returns of Option A and Option B is $-0\mathrm{.}3.$ Calculate the probability that the portfolio return, defined as $0\mathrm{.}3*$Option A $+0\mathrm{.}7*$Option B$,$ is less than $12\%.$

$6.$ You are analyzing a portfolio composed of two stocks: Stock X and Stock Y$.$ Stock X has an average annual return of $9\%$ with a standard deviation of $12\%,$ while Stock Y has an average annual return of $15\%$ with a standard deviation of $18\%.$ The correlation between the returns of Stock X and Stock Y is $0\mathrm{.}4.$ Determine the probability that the portfolio return, defined as $0\mathrm{.}5*$Stock X $+0\mathrm{.}5*$Stock Y$,$ exceeds $11\%.$