
Weight
Out of people attending a local gym, 10% are underweight, 20% are overweight, 15% are obese and the rest have normal weight. Underweight people on average weight 3kg less than their ideal weight, people within the normal weight range weigh on average 4kg more than the ideal weight, and overweight and obese people have 12 and 18 kg extra weight respectively. The standard deviation of the extra weight of the patrons of the gym is?

Have you any formulas or definitions?
First Moment: $\displaystyle a\;=\;E[X]\;=\;\sum{x \cdot p(x)}$
Second Moment: $\displaystyle b\;=\;E[X^{2}]\;=\;\sum{x^2 \cdot p(x)}$
$\displaystyle Variance(x)\;=\;b  a^{2}$
Is this ringing any bells?