Question 390747
{{{mu = 15}}} ===> {{{sigma^2 = E(X^2) - mu^2}}}, or 

{{{sigma^2 = (12^2*0.20 + 15^2*0.60 + 18^2*0.20) - 15^2 = 228.6 - 225 = 3.6}}}.  This is the variance of the distribution.  Its square root is the standard deviation, or {{{sigma = (3sqrt(10))/5 = 1.8974 }}}, to 4 decimal places.

{{{E(X^2) }}} means expectation, or the mean of the squares of the random variables. It does NOT mean the sum of squares.  After squaring each random variable value, you have to multiply each squared value with its corresponding probability.  Please read entirely the solution to the problem.