A machine is programmed to fill packets with 500 grams of nuts. It is known from previous experience the net weight of nuts in the packets are normally distributed with \(\mu=502\) grams and \(\sigma=3\) grams. A packet is considered conformant with the weight specifications if its net weight is at least 500 grams.

a. What proportion of the packets are considered conformant?

b. What proportion of the packets have a net weight of less than 510 grams?

c. What proportion of the packets have a net weight of less than 500 grams or more than 510 grams?

d. What is the median of the net weights of nuts in the packets?