The lifetime of a light bulb in a certain application is normally distributed with a mean = 1400 hours and standard deviation =

The lifetime of a light bulb in a certain application is normally distributed with a mean μ = 1400 hours and standard deviation σ = 200 hours. 

a. What is the probability that a randomly selected light bulb will last more than 1800 hours? 

b. Find the 10th percentile of the lifetimes. 

c. A particular light bulb lasts 1645 hours. What percentile is its lifetime on? 

d. What is the probability that the lifetime of a light bulb is between 1350 and 1550 hours? 

e. Eight light bulbs are chosen at random. What is the probability that exactly two of them have lifetimes between 1350 and 1550 hours. 

f. Eight light bulbs are chosen at random. What is the probability that the average lifetime of the eight light bulbs is between 1350 and 1450?