Sampling Distributions · Superchallenge problem

Light bulb lifetimes are strongly skewed, with mean $1000$ hours and SD $1000$ hours. Bulbs are used one after another, each replaced when it fails. Using the central limit theorem with $z = 1.645$, what is the smallest number of bulbs to stock so that the probability their total lifetime is at least $20{,}000$ hours is at least $0.95$?