The fan in a particular laptop used by a small department at Smartee University has an average lifespan of 12,000 hours.

a) Identify the distribution and parameter(s) of a fan's lifespan. What is the support?

b) What is the probability that a fan in a laptop will break before its average lifespan?

c) What is the probability that a fan in a laptop operates over 8,600 hours?

d) Given a fan has already operated for 10,000 hours, what's the probability that it will operate more than 14,500 hours total?

e) Given a fan operates no more than 15,000 hours, what's the probability that it breaks before 9,500 hours?

f) What is the median of a fan's lifespan?