The major stock market indexes had strong results in a recent year. The mean$$ one$-$year return for stocks in Index$$ A$,$ a group of very large$$ companies, was $11\mathrm{.}5\%.$ The mean$$ one$-$year return for stocks in Index$$ B$,$ a group of small and$$ medium$-$sized companies, was $15\mathrm{.}0\%.$Historically$,$ the$$ one$-$year returns are approximately normally$$ distributed, the standard deviation in Index A is approximately $19\%,$ and the standard deviation in Index B is approximately $38\%.$ What is the probability that a stock in Index A gained value in this$$ year?

Question $19$ options:

$0\mathrm{.}5312$

$0\mathrm{.}2725$

$0\mathrm{.}7275$

$0\mathrm{.}0145$