Question 1036225
Let x = the number of girls in a family with three children. Then the r.v. has pmf
{{{p(x) = (matrix(2,1,3,x))*0.64^(3-x)*0.36^x = 0.262144}}}, where x = 0,1,2,3.

{{{p(0) = (matrix(2,1,3,0))*0.64^3*0.36^0 = 0.262144}}}

{{{p(1) = (matrix(2,1,3,1))*0.64^2*0.36^1 = 0.442368}}}

{{{p(2) = (matrix(2,1,3,2))*0.64^1*0.36^2 = 0.248832}}}

{{{p(3) = (matrix(2,1,3,3))*0.64^0*0.36^3 = 0.046656}}}

Mean = {{{mu = np = 3*0.36 = 1.08}}} (Or practically, the mean number of girls in 3 children is 1, given the conditions.)

==>Standard deviation is {{{sigma = sqrt(npq) = sqrt(3*0.36*0.64) = 0.83}}} to two significant figures.

Under the given condition (p = 0.36), it is unusual for a family of 3 children to consist of 3 girls (chance is only 4.7%.)