Hi

I am new to this site and have joined hoping somebody could help me with some statistics problems I am having.

Basically, the question is:

Packets of crisps from a production line have a weight distribution that is normal with a mean of 50.0 grams and a standard deviation of 2.0 grams. Samples are taken of size 36.

What is the probability that a sample mean is less than 49.0 grams? (Give answer to four decimal places.)

What would be the control limits for a three standard error control chart in these circumstances? Give your answer in the format (to the nearest gram):

(25,72) grams

if you think these are the lower and upper limits

What proportion of sample means would be outside the these control limits? (Give your answer as a percentage, accurate to 0.1%

Thank you very much to anybody who answers - you have no idea how much you will be helping me!