Show that if x follows a binomial distribution with ni trials and probability of success pi = p, where i = 1; 2; : : : ; n, and the xi are independent, then pn i=1 xi follows a binomial distribution

the battle of gettysburg is considered the "high water mark" of the confederacy because it marked the greatest advance of the confederate forces against the union.

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.