Question 1164705
the means are 180 and 130
the variances are 400 and 225 (square sd)
the new distribution has mean of 310, the sum
and variance 625, the sum of the individual variance, which means the sd for the combined distribution is 25

so probability sum of the weights is less than 280 is 
z<(280-310)/25
z< -30/25 or -1.2
probability=0.1151