There is a stock that in the past has produced on average an

There is a stock that, in the past has produced, on average annual return of 3.7%, with a standard deviation of 2.9%. These returns are, you assume, normally distributed. You will invest $350 in this stock for one year. What is the probability that you will recieve a return worth at least $75?

-Please explain and show how problem was done!

Solution

Annual return is normal (3.7%, 2.9%)

For 350 invested,

return >=75

i.e. return percent >= 75/350 = 21.43

P(X>21.43%) = P(Z>17.73/2.9)

= P(Z>6.114)

= 0.0000