Linear combinations of random variable

I have no idea what I did wrong, please help!

Small packets of nails are advertised as having average weight 500 g, and large packets as having average weight 1000 g. Assume that the packet weight are distributed normally with means as advertised, and standard deviations of 10 g for a small packet and 15 gram for a large packet. Giving your answers correct to 3 decimal places.

a. find the probability of two randomnly chosen packets have a total weight between 990 gram and 1020 gram.

b. find the probability that the weight of one randomly chosen large packet exceeds the total weight of two randomly chosen small packets by at least 25 gram.

c. find the probability that one half of the weight of one randomly chosen large packet exceeds the weight of one randomly chosen small packet by at least 12.5 gram.

Re: Linear combinations of random variable

I was just answering this same question RIGHT NOW.

I also need help regarding this.

Why is it that the variance is sqr. root of 200 and not sqr root of 400? THIS IS WHAT I DO NOT UNDERSTAND.

When do we use : a^2 x Var(X) AND when do we use a x Var(X) ???

Please explain. Would highly appreciate an answer today. Have my finals tomorrow !