At King Kong High School, the average weight of senior boys is 168 lbs. with a standard deviation of 7 lbs. The average weight for senior girls is 117 libs. with a standard deviation of 5 lbs. Suppose a new distribution is created by adding the boys' weights and the girls' weights together. Assuming that the weights for boys and girls are independent, which of the following is true?

I. The mean of this new distribution is 168+117.
II. The standard deviation of this new distribution is 5+7.
III. The variance of this new distribution is 5^2+7^2

Question

At King Kong High School, the average weight of senior boys is 168 lbs. with a standard deviation of 7 lbs. The average weight for senior girls is 117 libs. with a standard deviation of 5 lbs. Suppose a new distribution is created by adding the boys' weights and the girls' weights together. Assuming that the weights for boys and girls are independent, which of the following is true? 

I. The mean of this new distribution is 168+117. 
II. The standard deviation of this new distribution is 5+7. 
III. The variance of this new distribution is 5^2+7^2

hockeychick23 · Answer

A. I and III only
B. II only
C. I and II only
D. I, II, and III
E. I only

hockeychick23 · Answer

@perl

hockeychick23 · Answer

@kropot72 @TuringTest @jim_thompson5910

mrnood · Answer

I THINK (but am not totally sure) that oyu need toknow what the 2 population sizes are before you merge them.

forinstance if there were 100 boys and 3 girls then the merged populatin would be very similar to the boys, but if there were 1000 of each then the  merge population would be between the two.

(NOTE - statistics not my strongest point - so please check....)

mrnood · Answer

THIS PAGE http://mathbench.umd.edu/modules/statistical-tests_t-tests/page05.htm suggests that you do not need the total population. you know that variance = sd^2 - so that page gives the answer.

hockeychick23 · Answer

@MrNood so does that make it I, II, and III?