Question 352210
Now that you have the mean, calculate the square of the difference between the x value and the mean, square it, and multiply by the probability.
{{{VAR=sum((x-mu)^2*P(x))}}}
.
.
{{{sigma=sqrt(sum((x-mu)^2*P(x)))}}}
.
.
{{{mu=8.46}}}
.
x1:{{{(3-8.46)^2*(0.15)=4.472}}}
x2:{{{(6-8.46)^2*(0.29)=1.755}}}
x3:{{{(9-8.46)^2*(0.30)=0.087}}}
x4:{{{(12-8.46)^2*(0.11)=1.378}}}
x5:{{{(15-8.46)^2*(0.15)=6.416}}}
Sum those values, that's the variance.

{{{VAR=14.108}}}
Take the square root of the variance, that's the standard deviation.
{{{STDEV=3.756}}}
Best way is to set up an EXCEL spreadsheet to crank through all of these operations.