Machine A produces components with holes whose diameter is normally distributed with a mean 56,000 and a standard deviation 10. Machine B produces components with holes whose diameter is normally distributed with a mean 56,005 and a standard deviation 8. Machine C produces pins whose diameter is normally distributed with a mean 55,980 and a standard deviation 10. Machine D produces pins whose diameter is normally distributed with a mean 55,985 and a standard deviation 9.
(a) What is the probability that a pin from machine C will have a larger diameter than a pin from machine D?
(b) What is the probability that a pin from machine C will fit inside the hole of a component from machine A?
(c) If a component is taken from machine A and a component is taken from machine B. what is the probability that both holes will be smaller than 55,995?