Central Limit Theorem and Exponential Distribution

[simplemts]

Exponential Distribution with lambda = 1/2. Use the central limit theorem to estimate the probability that the average service time of the first n customers is less than 2.5 minutes, when:
n = 16
n = 36
n = 100

After reviewing the chapter notes, I'm asked to estimate:
the probability that the average service time of the first n customers is less than 2.5 minutes, when:
n = 16, 36, 100.

Any hint on what formula or theorem to use for this?

[Dason]

Well you might want to see if you can apply the Central Limit Theorem to figure out the sampling distribution of the sample mean for this exponential distribution.