Hey all, first time poster, but I'm sure this won't be my only visit.
I'm in a discrete mathematics class, and am really stuck on this one problem. Basically, it goes as follows. There is a place, Bob's metal shed, that produces long metal tubes of size L for their customers. The customer specifies L, and n, the number of pieces, and they will receive n pieces of size between L-.5cm and L+.5cm. The length of the pieces cut has a variance of 1/16, and the cut length of the pieces follows a normal distribution. Produced pieces outside of the L-.5 to L+.5 range are defectives and are thrown out. The total number of pieces produced, both defective and not, is m.
So... I'm asked to find the probability that the machine produced a piece which can be delivered to the customer, using the cumulative distribution function for the standard normal RV. I know that the sigma^2 parameter is the variance, 1/16, and that mu, the expected value, would be mp, where p is the probability of an acceptable piece being made. p would be equal to n/m, and therefore mu is m*(n/m)=n. This is about where I get stuck... How do I go from that, to using the CDF to find the probability of one piece being acceptable? Preemptive thanks for the help!