a. A>B
b. A<B
c. A=B
d. Not enough info.
I chose D because 'normal distribution' is not written in the problem. Otherwise I would choose (b) because A = 42 and B > 48 (the different between -3σ and 3σ which is 114-66=48)
Please correct me if I'm wrong.
The answer is (d) according to the book, however, I don't understand any thing highlighted here:
So please elucidate it if you could. I really appreciate it!
The weight of $A$ is $90-2\cdot 8=74$ pounds. Bag $B$ weighs $90+5=95$ pounds. It is unfortunate that they use $A$ and $B$ again for quantities that are not the weight of these bags, but quantity $A$ is $2(95-74)=42$ pounds as you found (though it would have been good to specify that it was the quantity and not the bag weight)
To prove $D$ is correct, you could show two distributions that have the given mean and standard deviation, one with a range less than $42$ and one with a range greater than $42$. You need one bag with weight $74$ and one with weight $95$. The minimum range is $21$ from bags $A$ and $B$. You are $11$ pounds light for the average, so add in a bag at $101$ for a range of $37$ and enough bags at $90$ to bring the standard deviation down to $8$. For one with greater range, add in bags of weights $60$ and $131$, which gets a range of $71$ and an average of $90$. Again, add in enough bags at $90$ to bring the standard deviation down to $8$. It will take a bunch, but that is OK.