The sale price of a certain model of grand piano across the country is approximately normally distributed with a mean of $75,000 and a standard deviation of $5,300.

a)  What is the probability of a grand piano selling for more than $78,200 

b) Consider a set of 20 grand pianos. What is the probability that 4 or less of the pianos sell for more than $78,200?

c) As these pianos sell across the country, what is the probability that 4 pianos will need to be sold in order to sell one for more than $78,200? (The first piano that sells for more than $78,200 is the fourth piano.) 

d)  What is the probability of two randomly chosen grand pianos selling for more than $157,300 combined? 
Hint: Let Y=X+X

e) Consider two randomly chosen grand pianos. What is the probability that the first piano sold for at least $9,300 more than the second? 
Hint: Let Y=X-X