A type of capacitor has resistances that vary according to a normal distribution with a mean of 800 megohms and a standard deviation of 200 megohms (see Nelson, Industrial Quality Control, 1967, pp. 261-268, for a more thorough discussion). A certain application specifies capacitors with resistances between 900 and 1,000 megohms.
a What proportion of these capacitors will meet this specification?
b If two capacitors are randomly chosen from a lot of capacitors of this type, what is the probability that both will satisfy the specification?