A company that produces laundry detergent has a presentation of 500g detergent bags. The process of sending the pens is controlled and the weight per bag follows approximately a normal distribution with a measurement of 510gr and the standard deviation of 10gr and certain of the other bags.
a) Suppose you take 10 bags of detergent. What is the probability that the most one of those bags has a content less than 490gr?
b) The company delivers 100 bags to a store. How do you distribute the number of bags with less than 490? What is the probability that more than 2 bags have been filled with less than 490gr? If approximately distribution is necessary to answer the question.
My try:
a) We got $X$~$N(510, 10)$ so if we take the transformation $Z = \frac{X-u}{\sigma^2}$ then we got $Z$~$N(0, 1)$ which is easier to work with. But then I don´t know how to calculate the probability asked.
b) For be I belive that we got to use the moment generating function: $M_X(t)=e^{ut + \frac{\sigma^2t^2}{2}}$ but clearly in ordener to answer this question I need a)