Stndrd Dev of a probability

Help, please and thank you. 12. An analyst developed the following probability distribution of the rate of return for a common stock: Scenario Probability Rate of return Recession 0.20 -0.05 Normal 0.60 0.10 Boom 0.20 0.25 The standard deviation of the rate of return is closest to: A. 0.0090. B. 0.1003. C. 0.0949. D. 0.0010.

C First calculate the expected return: -0.2*5%+0.6*10%+0.2*25%=10% Then the standard deviation would be ((10-(-5))^2*0.2+(10-10)^2*0.6+(25-10)^2*0.2)^0.5=9.48683~9.49

thanks Map1, I was missing the prob in my stndrd dev calculation

when do we divide st. dev by n-1?

when n is provided to you. In the case they provide probability like in the problem above - the probability already includes the n in a manner of speaking.

with probability provided, variance = summation of P(Xi)*[X(i) - E(X)]^2